Question

What is the other endpoint of a segment with one endpoint at(-3, 8) and the midpoint at (7, 1)?​

Answer 1

Answer: The other point is (17, -6).

Explanation:

Midpoint (x,y) of the line segment joining (a,b) and (c,d) is given by :-

`(x,y) =((a+c)/(2), (b+d)/(2))`

Here, we need to find the other endpoint of a segment with one endpoint at(-3, 8) and the midpoint at (7, 1).

Let other point be (a,b), then

`(7,1)=((-3+a)/(2),(8+b)/(2))\\\\\Rightarrow\ (-3+a)/(2)=7\ \text{ and }(8+b)/(2)=1\\\\\Rightarrow\ -3+a = 7*2 \text{ and } 8+b=1*2\\\\\Rightarrow\ -3+a=14\text{ and }8+b=2\\\\\Rightarrow\ a=14+3, \ \ \ b= 2-8\\\\\Rightarrow\ a=17, b= -6`

hence, the other point is (17, -6).