A line intersects the y-axis and x-axis at the points P and Q respectively.If (2,-5) is the midpoint of PQ, then find the coordinates of P and Q.
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Answers
Given that,
- A line intersects the y-axis and x-axis at the points P and Q respectively and (2,-5) is the midpoint of PQ.
Let assume that
- Coordinates of point P be (0, a)
- Coordinates of point Q be (b, 0)
Now,
- (2, - 5) is the midpoint of PQ.
We know
Mid-point formula.
Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the mid-point of PQ. Then, the coordinates of R will be:
So, using Midpoint Formula, we get
So, on comparing, we get
So,
- Coordinates of point P be (0, - 10)
- Coordinates of point Q be (4, 0)
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More to know :-
1. Section formula.
Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the point which divides PQ internally in the ratio m₁ : m₂. Then, the coordinates of R will be:
2. Distance formula.
Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane, then distance between P and Q is
3. Centroid of a triangle.
Centroid of a triangle is the point where the medians of the triangle meet.
Let A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) be the vertices of a triangle. Let R(x, y) be the centroid of the triangle. Then, the coordinates of R will be: