Question

A line intersects the y-axis and x-axis at points P and Q respectively. If (2, -5) is the midpoint of PQ, then find the coordinates of points K and Q.

a) K: (0, -10), Q: (4, 0)

b) K: (2, -5), Q: (6, 5)

c) K: (4, 10), Q: (2, 0)

d) K: (0, 5), Q: (2, 0)

Answer 1

The correct coordinates for points P (also called K) and Q, given the midpoint (2, -5), are P: (0, -10) and Q: (4, 0). The student can determine this by setting up simple equations based on the properties of a midpoint, specifically that the midpoint's coordinates are the averages of the corresponding coordinates of the endpoints.

Step-by-step explanation:

The student is asking for help with a problem involving finding the coordinates of points where a line intersects the x-axis and y-axis, given the midpoint of the segment formed by those intersections. Since the midpoint of the line segment PQ is (2, -5), the x-coordinate of the midpoint is the average of the x-coordinates of P and Q, and the y-coordinate of the midpoint is the average of the y-coordinates of P and Q.

If the line intersects the y-axis at point P, the x-coordinate of P must be 0. Similarly, if the line intersects the x-axis at point Q, the y-coordinate of Q must be 0. So, the coordinates for P and Q are of the form (0, y) and (x, 0) respectively. Using the fact that (2, -5) is the midpoint, we can set up the equations:

1. 0 + x = 2*2
2. y + 0 = 2*(-5)

Solving these, we get x = 4 and y = -10.

Therefore, point P (also known as point K in the question) has coordinates (0, -10) and point Q has coordinates (4, 0). Option a is the correct answer: K: (0, -10), Q: (4, 0).