Question

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

Answer 1

Answer:

(-12 , 2)

Step-by-step 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 =

$(x , y) = (\frac{x^2 + x^1}{2} ,\frac{y^2 + y^1}{2} )$

PROCEDURE :-

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

So ,

$(-8 , -4) = (\frac{-4 + x}{2} , \frac{-10 + y}{2} )$

First , lets solve for x.

$=> \frac{x - 4}{2} = -8$

$=> x - 4 = -8 \times 2 = -16$

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

Now , lets solve for y.

$=> \frac{y - 10}{2} = -4$

$=> y - 10 = -4 \times 2 = -8$

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

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