Question

19. Elein and Naya wanted to meet between their

houses at midpoint (4,1). If Elien's house is at point
A. (7,-1.5)
(10,-4).
B. (-2,6)
Find the coordinates of Naya's house.
C. (0,0)

Answer 1

`(-2,6)`

Explanation:

Given

`Elena = (10,-4)`

`Midpoint = (4,1)`

Required

Determine the coordinates of Naya's

Midpoint is calculated as:

`M(x,y) = (1)/(2)(x_1+x_2,y_1+y_2)`

In this case:

`(x_1,y_1) = (10,-4)`

`(x,y) = (4,1)`

So, we have:

`(4,1) = (1)/(2)(10+x_2,-4+y_2)`

Multiply through by 2

`2 * (4,1) = (1)/(2)(10+x_2,-4+y_2) * 2`

`(8,2) = (10+x_2,-4+y_2)`

By comparison:

`8 = 10 + x_2`

`2 = -4 + y_2`

So:

`8 = 10 + x_2`

`x_2 = 8 - 10`

`x_2 = -2`

`2 = -4 + y_2`

`y_2 =2+4`

`y_2 =6`

So, the coordinate is:
`(-2,6)`