Mathematics : asked on xeno777

23.09.2021

What elements do you need to show to confirm that Point L is on the Perpendicular Bisector of JK?

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Mathematics

If JK is formed by J(-7,-8) & K(1,4), determine if L(-9,5), lies on the perpendicular bisector. Part A: What elements do you you need to know to confirm that Point L is on the perpendicular bisector of JK? Part B: Find the elements you described in Part A , explain your work. Part C: Verify if Point L is on the perpendicular bisector of JK. Justify your conclusion.

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P Answered by Specialist

Following are the responses to the given question:

Step-by-step explanation:

For point a:

Bisector Theorem: When a point has been on the perpendicular bisector of a segment, the perpendicular bisector is equivalent towards the segment endpoints. They understand that conversation also valid in addition to the Theorem including its perpendicular bisector. So the distance b/w L and J, L, and k must be found. Examine it then.

For point b:

Calculating the distance among two point:

$d_0 = \sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}$

Calculating the distance among J and L

$d_1 = \sqrt{((-9)-(-7))^2 + (5)-(-8))^2}$

$=\sqrt{(-2)^2+(13)^2}\\\\ = \sqrt{173}$

Calculating the distance among K and L

$d_2 = \sqrt{((-9)-(1))^2 + (5)-(4))^2}$

$=\sqrt{(10)^2+(1)^2}\\ = \sqrt{101}$

For point c:

As these two distances are not equal, L doesn't really lie on the JK bisector.

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