Mathematics: Line f and g and points P and Q are graphed on this coordinate plane. The equation of line f is y=2. The equation of line g is y=2x-1

A) Equation of line parallel to f and passes through P A line parallel to x-axis is y = k y = -1 B)...

Line f and g and points P and Q are graphed on, №15226776, 01.07.2021 22:40

Mathematics

Square PQRS is rotated 90° clockwise using the origin as the center of rotation. On a coordinate plane, square P Q R S has points (negative 2, 2), (negative 2, negative 1), (1, negative 1), (1, 2). Which graph shows the image P’Q’R’S’? On a coordinate plane, square P prime Q prime R prime S prime has points (2, 2), (negative 1, 2), (negative 1, negative 1), (2, negative 1). On a coordinate plane, square P prime Q prime R prime S prime has points (negative 1, negative 1), (2, negative 1), (2, 2), (negative 1, 2). On a coordinate plane, square P

Step-by-step answer

P Answered by PhD

23

Option 3:

On a coordinate plane, square P prime Q prime R prime S prime has points (negative 2, negative 2), (1, negative 2), (1, 1), (negative 2, 1).

Step-by-step explanation:

After 90° clockwise rotation,

(x,y) ---> (-y,x)

(negative 2, 2) ---> (-2,-2)

(negative 2, negative 1) ---> (1,-2)

(1, negative 1) ---> (1,1)

(1, 2) ---> (-2,1)

Mathematics

Square PQRS is rotated 90° clockwise using the origin as the center of rotation. On a coordinate plane, square P Q R S has points (negative 2, 2), (negative 2, negative 1), (1, negative 1), (1, 2). Which graph shows the image P’Q’R’S’? On a coordinate plane, square P prime Q prime R prime S prime has points (2, 2), (negative 1, 2), (negative 1, negative 1), (2, negative 1). On a coordinate plane, square P prime Q prime R prime S prime has points (negative 1, negative 1), (2, negative 1), (2, 2), (negative 1, 2). On a coordinate plane, square P

Step-by-step answer

P Answered by PhD

23

Option 3:

On a coordinate plane, square P prime Q prime R prime S prime has points (negative 2, negative 2), (1, negative 2), (1, 1), (negative 2, 1).

Step-by-step explanation:

After 90° clockwise rotation,

(x,y) ---> (-y,x)

(negative 2, 2) ---> (-2,-2)

(negative 2, negative 1) ---> (1,-2)

(1, negative 1) ---> (1,1)

(1, 2) ---> (-2,1)

Mathematics

Figure qrts is reflected about the y-axis to obtain figure q’r’t’s’: a coordinate plane with two quadrilaterals is shown. figure qrts has vertices q at negative 5 comma 3, r at negative 5 comma 1, s at negative 2 comma 2 and t at negative 2 comma 0. figure q prime r prime t prime s prime has vertices q prime at 5 comma 3, r prime at 5 comma 1, s prime at 2 comma 2 and t prime at 2 comma 0. which statement best describes the relationship between the two figures? figure qrts is bigger than figure q’r’t’s’. figure qrts is congruent to figure q’r’ts’.

Step-by-step answer

P Answered by Specialist

The correct option is B) Figure QRTS is congruent to figure Q’R’TS’. But reflected about the y axis.

Step-by-step explanation:

Consider the provided information,

Now, draw the quadrilaterals with the help of provided information.

The figure 1 shows the two quadrilaterals.

Now, consider the provided options.

Option A is wrong because QRTS is not bigger than figure Q’R’T’S.

Option B is correct because Figure QRTS is congruent to figure Q’R’TS’. But reflected about the y axis.

Option C is wrong because measure of angle R is not equal to the measure of angle Q’. Measure of angle R is equal to the measure of angle R’.

Option D is wrong because the measure of angle S is not equal to the measure of angle T’. The measure of angle S is equal to the measure of angle S’.

Hence, the correct option is B) Figure QRTS is congruent to figure Q’R’TS’. But reflected about the y axis.

Figure qrts is reflected about the y-axis to obtain figure q’r’t’s’: a coordinate plane with two qu

Mathematics

Manuela claims that Segment A B and Segment P Q are congruent. On a coordinate plane, segment P Q goes from (negative 3, negative 1) to (negative 3, 3) and segment A B goes from (0, 1) to (3, 1). Which statement best describes her claim? She is incorrect because the segments do not have the same orientation. She is incorrect because the segments do not have the same length. She is correct because the segments have the same length. She is correct because the segments have the same orientation.

Step-by-step answer

P Answered by PhD

27

B.She is incorrect because the segments do not have the same length.

Step-by-step explanation:

We are given that

Manuela claims that segment AB and segment PQ are congruent.

When two segment are congruent the their lengths are equal.

PQ passing through the point (-3,-1) and (-3,3)

Length of PQ= $\sqrt{(-3+3)^2+(3+1)^2}=4 units$

By using distance formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB passing through the points (0,1) and (3,1).

Length of AB= $\sqrt{(3-0)^2+(1-1)^2}=3units$

Length of AB is not equal to length of PQ.

Option B is true.

She is incorrect because the segments do not have the same length.

Mathematics

A line contains L(-4, -4) and M(2,3). Line q is in the same coordinate plane but does not intersect LM. Line q contains point N.

Step-by-step answer

P Answered by Master

A general line equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we will find that for N(x₁, y₁), the line q is:

$y = \frac{7}{6}*x + (y_1 - \frac{7}{6}*x_1)$

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

In this case, we know that the line passes through (-4, -4) and (2, 3), then the slope is:

$a = \frac{3 - (-4)}{2 - (-4)} = \frac{7}{6}$

So the line is something like:

$y = \frac{7}{6} *x + b$

To find the value of b, we can use one of the two points, for example (2, 3) means that when x = 2, y must be equal to 3, then we can replace these two in the line equation to get:

$3 = \frac{7}{6}*2 + b\\\\3 = \frac{7}{3} + b\\\\3 - \frac{7}{3} = b = 2/3$

Then the line LM is;

$y = \frac{7}{6}*x + \frac{2}{3}$

Now we know that line q is in the same coordinate plane, but does not intersect LM. This means that these lines are parallel, and remember that two parallel lines have the same slope, then the slope of line q is also 7/6.

Now we know that line q passes through point N, but we do not know the coordinates of point N, then let's use general coordinates as N(x₁, y₁)

Then line q will be:

$y = \frac{7}{6}*x + c$

To find the value of c we use the point N.

$y_1 = \frac{7}{6}*x_1 + c\\\\y_1 - \frac{7}{6}*x_1 = c$

Then the equation of line q is:

$y = \frac{7}{6}*x + (y_1 - \frac{7}{6}*x_1)$

If you want to learn more, you can read:

Mathematics

Manuela claims that Segment A B and Segment P Q are congruent. On a coordinate plane, segment P Q goes from (negative 3, negative 1) to (negative 3, 3) and segment A B goes from (0, 1) to (3, 1). Which statement best describes her claim? She is incorrect because the segments do not have the same orientation. She is incorrect because the segments do not have the same length. She is correct because the segments have the same length. She is correct because the segments have the same orientation.

Step-by-step answer

P Answered by PhD

27

B.She is incorrect because the segments do not have the same length.

Step-by-step explanation:

We are given that

Manuela claims that segment AB and segment PQ are congruent.

When two segment are congruent the their lengths are equal.

PQ passing through the point (-3,-1) and (-3,3)

Length of PQ= $\sqrt{(-3+3)^2+(3+1)^2}=4 units$

By using distance formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB passing through the points (0,1) and (3,1).

Length of AB= $\sqrt{(3-0)^2+(1-1)^2}=3units$

Length of AB is not equal to length of PQ.

Option B is true.

She is incorrect because the segments do not have the same length.

Mathematics

Calculate the distance between the points J= (2, -3) and Q=(9,-9) in the coordinate plane. Round your answer to the nearest hundredth.

Step-by-step answer

P Answered by Specialist

9.22

Step-by-step explanation:

First, let's establish the distance formula! The distance formula is $d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2$ . Now, let's input our variables into the formula.

$d = \sqrt{(9-2)^2 + (-9 + 3)^2}$ (Also, we changed the minus sign to a plus sign because we have a negative number and we know that a negative minus a negative is a positive!) Now we can start to solve the equations!

1st. We need to solve inside the parenthesis of both the x parenthesis and the y parenthesis.

$d = \sqrt{(7)^2 + (-6)^2}$

2nd. We should square the inside of both of the parenthesis!

$d = \sqrt{49 + 36$ (Remeber that when you square a negative you get a positive)

3rd. Then, we can add 49 and 36!

$d = \sqrt{85}$

4th. Lastly, we are going to find the square root of 85.

d ≈ 9.22 (Remember that "≈" means the round solution, in this case we are rounding to the nearest 100th!)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Mathematics

Calculate the distance between the points k=-7,9 and q= -4,3 in the coordinate plane. round your answer to the nearest hundredth.

Step-by-step answer

P Answered by PhD

2

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ K(\stackrel{x_1}{-7}~,~\stackrel{y_1}{9})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ KQ=\sqrt{[-4-(-7)]^2+[3-9]^2}\implies KQ=\sqrt{(-4+7)^2+(3-9)^2} \\\\\\ KQ=\sqrt{3^2+(-6)^2}\implies KQ=\sqrt{45}\implies KQ\approx 6.71$

Mathematics

Calculate the distance between the points J= (2, -3) and Q=(9,-9) in the coordinate plane. Round your answer to the nearest hundredth.

Step-by-step answer

P Answered by Master

9.22

Step-by-step explanation:

First, let's establish the distance formula! The distance formula is $d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2$ . Now, let's input our variables into the formula.

$d = \sqrt{(9-2)^2 + (-9 + 3)^2}$ (Also, we changed the minus sign to a plus sign because we have a negative number and we know that a negative minus a negative is a positive!) Now we can start to solve the equations!

1st. We need to solve inside the parenthesis of both the x parenthesis and the y parenthesis.

$d = \sqrt{(7)^2 + (-6)^2}$

2nd. We should square the inside of both of the parenthesis!

$d = \sqrt{49 + 36$ (Remeber that when you square a negative you get a positive)

3rd. Then, we can add 49 and 36!

$d = \sqrt{85}$

4th. Lastly, we are going to find the square root of 85.

d ≈ 9.22 (Remember that "≈" means the round solution, in this case we are rounding to the nearest 100th!)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Mathematics

Calculate the distance between the points k=-7,9 and q= -4,3 in the coordinate plane. round your answer to the nearest hundredth.

Step-by-step answer

P Answered by PhD

2

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ K(\stackrel{x_1}{-7}~,~\stackrel{y_1}{9})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ KQ=\sqrt{[-4-(-7)]^2+[3-9]^2}\implies KQ=\sqrt{(-4+7)^2+(3-9)^2} \\\\\\ KQ=\sqrt{3^2+(-6)^2}\implies KQ=\sqrt{45}\implies KQ\approx 6.71$

Line f and g and points P and Q are graphed on this coordinate plane. The equation of line f is y=2. The equation of line g is y=2x-1

Step-by-step answer

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