Question

Given the midpoint and one endpoint of a line segment, find the other endpoint.

Endpoint: (-4,-10), midpoint: (-8,-4)

Answer 1

(-12 , 2)

Explanation:

GIVEN :-

• Co-ordinates of one endpoint = (-4 , -10)
• Co-ordinates of the midpoint = (-8 , -4)

TO FIND :-

• Co-ordinates of another endpoint.

FACTS TO KNOW BEFORE SOLVING :-

Section Formula :-

Let AB be a line segment where co-ordinates of A = (x¹ , y¹) and co-ordinates of B = (x² , y²). Let P be the midpoint of AB . So , by using section formula , the co-ordinates of P =

`(x , y) = ((x^2 + x^1)/(2) ,(y^2 + y^1)/(2) )`

PROCEDURE :-

Let the co-ordinates of another endpoint be (x , y)

So ,

`(-8 , -4) = ((-4 + x)/(2) , (-10 + y)/(2) )`

First , lets solve for x.

`=> (x - 4)/(2) = -8`

`=> x - 4 = -8 * 2 = -16`

`=> x = -16 + 4 = -12`

Now , lets solve for y.

`=> (y - 10)/(2) = -4`

`=> y - 10 = -4 * 2 = -8`

`=> y = -8 + 10 = 2`

∴ The co-ordinates of another endpoint = (-12 , 2)