Question

K is the midpoint of PQ, P has

coordinates (-9,-4), and K
has coordinates (-1, 6). What
are the coordinates of Q?
A (-5, 1) C (-11,8)
B (5, 10) D (7.16)

Answer 1

Coordinates of Q
`(x_2,y_2) \:are\: \mathbf{(7,16)}`

Option D is correct option.

Explanation:

We are given:

K is the midpoint of PQ

Coordinates of P = (-9,-4)

Coordinates of K = (-1,6)

We need to find coordinates of Q
`(x_2,y_2)`

We will use the formula of midpoint:
`Midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))`

We are given midpoint K and
`x_1,y_1` the coordinates of P we need to find
`x_2,y_2` the coordinates of Q.

`Midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))\\(-1,6)=((-9+x_2)/(2),(-4+y_2)/(2))\\`

Now, we can write

`-1=(-9+x_2)/(2), 6=(-4+y_2)/(2)\\Simplifying:\\-2=-9+x_2\:,\: 12=-4+y_2\\-2+9=x_2\:,\: 12+4=+y_2\\x_2=7\:,\:y_2=16`

So, we get coordinates of Q
`(x_2,y_2) \:are\: \mathbf{(7,16)}`

Option D is correct option.