Question

B is the midpoint of AC, E is the midpoint of BD. If A(-9,-4), C(-1,6), and E(-4,-3), find the coordinates of D

Answer 1

(-3, -7)

Explanation:

Let
`(x_(A,)y_(A)),(x_(B),y_(B)),(x_(C,)y_(C)),(x_(D,)y_(D))(x_(E,)y_(E)) \text{be the coordinates of points A, B, C respectively}\\\\`

The midpoint coordinates
`(x_(M),y_(M))` of any two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` are given by
`x_(M)=((x_(1)+x_(2)))/(2)` and
`y_(M)=(y_(1)+y_(2))/(2)`

Since B is the midpoint of AC

`x_(B)=((x_(A)+x_(C)))/(2)=((-9+(-1))/(2)=(-9-1)/(2)=(-10)/(2)=-5`

`y_(B)=((y_(A)+y_(C)))/(2)=((-4+6))/(2)=(2)/(2)=1`

Since E is the midpoint of B and D and we are given the coordinates of E as (-4,-3). it follows that

`x_(E)=(x_(B)+x_(D))/(2) = (-4+x_(D))/(2)`

Therefore

`x_(D)=2x_(E)+4=2(-5)+4=-3`

Similarly

`y_(E)=(y_(B)+y_(D))/(2) = (1+x_(D))/(2)y_(D)=2y_(E)-1=2(-3)-7=-7`