Question

In a coordinate plane, the midpoint of AB is (2,5) and A is located at (-5,10). If (x,y) are the coordinates of B, find x and y.

Answer 1

In a coordinate plane, the midpoint of AB is (2,5) and A is located at (-5,10). If (x,y) are the coordinates of B, find x and y.​

Remember that

the formula to calculate the midpoint between two points is equal to

`M=((x1+x2)/(2),(y1+y2)/(2))`

In this problem we have

M=(2,5)

(x1,y1)=A(-5,10)

(x2,y2)=B(x,y)

substitute the given values

`(2,5)=((-5+x)/(2),(10+y)/(2))`

step 1

Find the x-coordinate of B

equate the x-coordinates

so

2=(-5+x)/2

solve for x

4=-5+x

x=4+5=9

step 2

Find the y-coordinate of B

equate the y-coordinates

5=(10+y)/2

solve for y

10=y+10

y=0

therefore

the coordinates of B are (9,0)