Question

The midpoint of PQ is (–6, –3). One endpoint of PQ is P(–1, –4). What are the coordinates of Q? A. Q(–11, –2) B. Q(–3.5, –3.5) C. Q(2, 11) D. Q(11, 2)

Answer 1

By using the midpoint formula, the coordinates of point Q are determined to be Q(–11, –2), matching option A.

Step-by-step explanation:

The student is tasked to find the coordinates of point Q if the midpoint of segment PQ is known to be (–6, –3) and one of the endpoints, P, is given as (–1, –4). To find the coordinates of the other endpoint, Q, we can use the midpoint formula which states that the midpoint is the average of the x-coordinates and y-coordinates of the endpoints:

M = \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)

Given M = (–6, –3) and P = (–1, –4), we can set them into the equation:

(–6, –3) = \( \left( \frac{–1 + x_Q}{2}, \frac{–4 + y_Q}{2} \right) \)

Solving the equations separately for x and y, we get:

x_Q = –6 * 2 + 1 = –12 + 1 = –11
y_Q = –3 * 2 + 4 = –6 + 4 = –2

Therefore, the coordinates of Q are Q(–11, –2), which corresponds to option A.

Answer 2

The coordinates of the midpoint of the line segment is the average of the coordinates of both end points. For this example above, let (x, y) be the coordinates of point Q.

(abscissa) -6 = (-1 + x) / 2 ; x = -11
(ordinate) -3 = (-4 + y) / 2 ; y = -2

Therefore, the coordinates of point Q is (-11, -2). The answer is letter A.