K is the midpoint of PQ, P has

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

6 0

Answer:

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

Option D is correct option.

Step-by-step 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: $Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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.

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\(-1,6)=(\frac{-9+x_2}{2},\frac{-4+y_2}{2})\\$

Now, we can write

$-1=\frac{-9+x_2}{2}, 6=\frac{-4+y_2}{2}\\Simplifying:\\-2=-9+x_2\:,\: 12=-4+y_2\\-2+9=x_2\:,\: 12+4=+y_2\\x_2=7\:,\:y_2=16$

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

Option D is correct option.

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