P and Q are the points on the line segment joining the points A(3, -1) and B(-6, 5) such that AP = PQ = QB. Find the coordinates of P and Q.

Given, AP = PQ = QB ∴ P divides AB in the ratio of 1 : 2 and Q divides it in 2 : 1. Let coordinates of P be (a, b) and of Q be (c, d) Applying section formula for x coordinate of P we get, Similarly, applying section formula for y coordinate of P we get, ∴ Coordinates of P = (a, b) = (0, 1). Applying section formula for x coordinate of Q we get, Similarly, applying section formula for y coordinate of Q we get, ∴ Coordinates of Q = (c, d) = (-3, 3). Hence, coordinates of P = (0, 1) and Q = (-3, 3).

Find the coordinates of the point that divides the line segment joining the points P(5, -2) and Q(9, 6) internally in the ratio of 3 : 1.

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Find the coordinates of the point P which is three-fourth of the way from A(3, 1) to B(-2, 5).

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The center of a circle is (α + 2, α - 5). Find the value of α, given that the circle passes through points (2, -2) and (8, -2).

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The mid-point of the line segment joining A(2, p) and B(q, 4) is (3, 5). Calculate the values of p and q.

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Mathematics

P and Q are the points on the line segment joining the points A(3, -1) and B(-6, 5) such that AP = PQ = QB. Find the coordinates of P and Q.

Section Formula

Related Questions

Find the coordinates of the point that divides the line segment joining the points P(5, -2) and Q(9, 6) internally in the ratio of 3 : 1.

Find the coordinates of the point P which is three-fourth of the way from A(3, 1) to B(-2, 5).

The center of a circle is (α + 2, α - 5). Find the value of α, given that the circle passes through points (2, -2) and (8, -2).

The mid-point of the line segment joining A(2, p) and B(q, 4) is (3, 5). Calculate the values of p and q.