# 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. - Mathematics

#### Question

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

Suppose the line intersects the y-axis at P(0, y) and the x-axis at Q(x, 0)

It is given that (2, –5) is the mid-point of PQ

Using mid-point formula, we have

((x+0)/2 , (0+y)/2) = (2, -5)

=> (x/2,y/2) = (2, -5)

=> x/2 = 2 and y/2 = -5

=> x = 4, y = - 10

Thus, the coordinates of P and Q are (0, −10) and (4, 0), respectively.

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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. Concept: Concepts of Coordinate Geometry.