Question

The midpoint of AD is C. The midpoint of AC is B. If A is at (-10,4) and D is at (2,12), find the coordinates of B. Group of answer choices (-5,5) (-4,8) (-2.5,9) (7,6)

Answer 1

`B(x,y) =(-7,6)`

Explanation:

Given

`A = (-10,4)`

`D = (2,12)`

Required

Determine the coordinates of B

C is the midpoint of AD. So, we calculate the coordinates of C, first.

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

Where:

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

`D = (2,12)` ---
`(x_2,y_2)`

So, we have:

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

`C(x,y) = ((-10+2)/(2),(4+12)/(2))`

`C(x,y) = ((-8)/(2),(16)/(2))`

`C(x,y) = (-4,8)`

So, the coordinates of C is (-4,8)

The midpoint of AC is B.

So, we calculate the coordinates of B using:

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

Where:

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

`C(x,y) = (-4,8)` ---
`(x_2,y_2)`

So, we have:

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

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

`B(x,y) =((-14)/(2),(12)/(2))`

`B(x,y) =(-7,6)`

Hence, the coordinates of B is (-7,6)

None of the options is correct.