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

Question

Answer

Answer

Answer

Coordinate of P (4,0) and coordinate of Q (0,-10)

Answer

Problem:
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q?

Solution:
To find the coordinates of points P and Q, we need to consider the given information that (2, -5) is the midpoint of the line segment PQ.

Step 1: Understanding the Midpoint Formula:
The midpoint of a line segment is the point that divides the segment into two equal parts. The midpoint formula can be used to find the coordinates of the midpoint (x, y) when we know the coordinates of the endpoints (x1, y1) and (x2, y2) of the line segment.

The midpoint formula is given by:
x = (x1 + x2) / 2
y = (y1 + y2) / 2

Step 2: Applying the Midpoint Formula:
Let's assume the coordinates of point P as (xP, 0) and the coordinates of point Q as (0, yQ), since P lies on the y-axis and Q lies on the x-axis.

Using the midpoint formula, we can set up two equations based on the given information:
xP + 0 / 2 = 2 ...(1)
0 + yQ / 2 = -5 ...(2)

Simplifying equations (1) and (2), we get:
xP / 2 = 2
yQ / 2 = -5

Multiplying both equations by 2 to eliminate the fractions, we get:
xP = 4
yQ = -10

Therefore, the coordinates of point P are (4, 0) and the coordinates of point Q are (0, -10).

Conclusion:
Hence, the coordinates of points P and Q are (4, 0) and (0, -10) respectively.

Answer

P(4,0) and Q(0,-10)

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