Question

PLEASE HELP ASAP!!! VERY IMPORTANT

Point M is the midpoint of PQ. The coordinates of P and M are given below.

M(5,-2) and P(11,-10)

Based on this information what are the coordinates of Q?

Show all work and provide any necessary descriptions.

Answer 1

Q(-1,6)

Explanation:

The midpoint rule is given as:

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

We have that point M is the midpoint of PQ and M(5,-2) and P(11,-10).

We substitute x=5, y=-2,
`x_1=11` and
`x_1=-10`.

`M(5,-2)=((11+x_2)/(2),(-10+y_2)/(2)  )`

This implies that:

`5=(11+x_2)/(2)`

`\implies 10=11+x_2`

`\implies x_2=-1`

`-2=(-10+y_2)/(2)`

`\implies -4=-10+y_2`

`\implies y_2=6`

Therefore the coordinates of Q are (-1,6)