Question

Kis the midpoint of PO, P has coordinates (-9 -4), and K has coordinates (-1,6). What are the coordinates of Q?

Answer 1

To find the coordinates of Q, we use the midpoint formula, resulting in Q having coordinates (7, 16).

Step-by-step explanation:

To find the coordinates of point Q in the line segment PO where K is the midpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the averages of the coordinates of the endpoints. Given that P has coordinates (-9, -4) and K has coordinates (-1, 6), we can set up the following equations:

• x-coordinate of K is the average of the x-coordinates of P and Q: (-9 + x_Q) / 2 = -1

• y-coordinate of K is the average of the y-coordinates of P and Q: (-4 + y_Q) / 2 = 6

Solving these equations will give us the coordinates of Q.

For the x-coordinate:

(-9 + x_Q) / 2 = -1

x_Q - 9 = -2 (Multiply both sides by 2)

x_Q = 7 (Add 9 to both sides)

For the y-coordinate:

(-4 + y_Q) / 2 = 6

y_Q - 4 = 12 (Multiply both sides by 2)

y_Q = 16 (Add 4 to both sides)

Therefore, the coordinates of point Q are (7, 16).