Suppose AB has one endpoint at A(0, 0). What, №14458424, 19.09.2022 01:14

Mathematics

Suppose line segment AB has one endpoint at A(0, 0). What are the coordinates of B if (5, 3) is 1/3 of the way from A to B?

Step-by-step answer

P Answered by PhD

1

Given:

Line segment AB has one endpoint at A(0,0).

(5, 3) is 1/3 of the way from A to B.

To find:

The coordinates of point B.

Solution:

Let the coordinates of point B are (a,b).

Suppose point P(5, 3) is 1/3 of the way from A to B.

$\dfrac{AP}{AB}=\dfrac{1}{3}$

$\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}=\dfrac{1}{3-1}=\dfrac{1}{2}$

It means, point P(5, 3) divides the segment AB in 1:2.

Section formula:

If a point divides a line segment in m:n, then

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Point P(5, 3) divides the segment AB in 1:2. Using section formula, we get

$P=\left(\dfrac{1(a)+2(0)}{1+2},\dfrac{1(b)+2(0)}{1+2}\right)$

$(5, 3)=\left(\dfrac{a}{3},\dfrac{b}{3}\right)$

On comparing both sides, we get

$\dfrac{a}{3}=5$

a=15

$\dfrac{b}{3}=3$

b=9

Therefore, the coordinates of point B are (15,9).

Mathematics

Suppose line segment AB has one endpoint at A(0, 0). What are the coordinates of B if (5, 3) is 1/3 of the way from A to B?

Step-by-step answer

P Answered by PhD

1

B(x_2,y_2)= (20,12)

Step-by-step explanation:

Given

A = (0,0)

Ratio; m : n = 1 : 3

$Point\ at\ 1 : 3 = (5,3)$

Required

Coordinates of B

This question will be answered using line ratio formula;

$(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})$

In this case:

(x,y) = (5,3)

(x_1,y_1) = (0,0)

m : n = 1 : 3

Solving for (x_2,y_2)

$(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})$ becomes

$(5,3) = (\frac{1 * x_2 + 3 * 0}{1 + 3},\frac{1 * y_2 + 3 * 0}{1 + 3})$

$(5,3) = (\frac{x_2 + 0}{4},\frac{y_2 + 0}{4})$

$(5,3) = (\frac{x_2}{4},\frac{y_2}{4})$

Comparing the right hand side to the left;

$\frac{x_2}{4} = 5$ -- (1)

$\frac{y_2}{4} = 3$ -- (2)

Solving (1)

x_2 = 5 * 4

x_2 = 20

Solving (2)

y_2 = 3 * 4

y_2 = 12

Hence;

B(x_2,y_2)= (20,12)

Mathematics

HELP ME QUICK: Suppose AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what are the coordinates of point B?

Step-by-step answer

P Answered by PhD

4

B(10, 6)

Step-by-step explanation:

If P is midpoint of AB and: $A(0,\,0)\,,\quad P(5,\,3)\,,\quad B(x_B,\,y_B)$

then:

$x_P-x_A=x_B - x_P\qquad\quad\ \wedge\qquad y_P-y_A=y_B - y_P\\\\ 5-0=x_B-5\qquad\quad\wedge\qquad 3-0=y_B -3\\\\ x_B=5+5\qquad\qquad\wedge\qquad\ \ y_B=3+3 \\\\ {}\quad x_B=10\qquad\qquad\wedge\qquad\qquad \ y_B=6$

Mathematics

Suppose AB has one endpoint at A(0,0). If (3, 4) is the midpoint of AB, what are the coordinates of your B?

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

(x + 0)/2 = 3

x + 0 =6

x = 6

(y + 0)/2 = 4

y + 0 = 8

y = 8

(6, 8)

Mathematics

HELP ASAP !! Suppose line segment AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what are the coordinates of point B?

Step-by-step answer

P Answered by Master

8

Step-by-step explanation:

what was the answer

Mathematics

HELP ME QUICK: Suppose AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what are the coordinates of point B?

Step-by-step answer

P Answered by PhD

4

B(10, 6)

Step-by-step explanation:

If P is midpoint of AB and: $A(0,\,0)\,,\quad P(5,\,3)\,,\quad B(x_B,\,y_B)$

then:

$x_P-x_A=x_B - x_P\qquad\quad\ \wedge\qquad y_P-y_A=y_B - y_P\\\\ 5-0=x_B-5\qquad\quad\wedge\qquad 3-0=y_B -3\\\\ x_B=5+5\qquad\qquad\wedge\qquad\ \ y_B=3+3 \\\\ {}\quad x_B=10\qquad\qquad\wedge\qquad\qquad \ y_B=6$

Mathematics

HELP ME QUICK: Suppose AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what are the coordinates of point B?

Step-by-step answer

P Answered by PhD

2

Step-by-step explanation:

Let the coordinates of B be (x,y)

$5=\frac{0+x}{2}\\x=5 \times 2=10\\3=\frac{0+y}{2}\\y=3 \times 2=6\\so~B~is~(10,6)$

Mathematics

Suppose AB has one endpoint at A(0,0). If (3, 4) is the midpoint of AB, what are the coordinates of your B?

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

(x + 0)/2 = 3

x + 0 =6

x = 6

(y + 0)/2 = 4

y + 0 = 8

y = 8

(6, 8)

Mathematics

Choose all that correctly define the point on the directed line segment between the two given points that partitions the segment in the given ratio. Line segment AB has endpoints A(8, 4) and B(4, 8). The coordinates (7, 5) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(1, 2) and B(9, 10). The coordinates (4, 3) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(1, 3) and B(5, 15). The coordinates (6, 2) divides the line segment directed from A to

Step-by-step answer

P Answered by Specialist

5

A(1, 3) and B(5, 15). The coordinates (6, 2) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(0, 12) and B(8, 8). The coordinates (2, 11) divides the line segment directed from A to B in the ratio of 1:3.

Step-by-step explanation:

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Mathematics

Choose all that correctly define the point on the directed line segment between the two given points that partitions the segment in the given ratio. Line segment AB has endpoints A(8, 4) and B(4, 8). The coordinates (7, 5) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(1, 2) and B(9, 10). The coordinates (4, 3) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(1, 3) and B(5, 15). The coordinates (6, 2) divides the line segment directed from A to

Step-by-step answer

P Answered by Specialist

5

A(1, 3) and B(5, 15). The coordinates (6, 2) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(0, 12) and B(8, 8). The coordinates (2, 11) divides the line segment directed from A to B in the ratio of 1:3.

Step-by-step explanation:

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Suppose AB has one endpoint at A(0, 0).
What are the coordinates of B if (5, 3) is 13
1
3 of the way from A to B

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Suppose AB has one endpoint at A(0, 0). What are the coordinates of B if (5, 3) is 13 1 3 of the way from A to B

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Try asking the Studen AI a question.

Suppose AB has one endpoint at A(0, 0).
What are the coordinates of B if (5, 3) is 13
1
3 of the way from A to B