Question

Find the point on PQ that divides the line segment directed from P to Q into the ratio of 1:3.

a) (5/2, 3)
b) (5/2, 5)
c) (11/2, 3)
d) (11/2, 5)

Answer 1

To find the point on PQ that divides the line segment directed from P to Q into the ratio of 1:3, we can use the section formula. The coordinates of the point are (5/2, 3).

Step-by-step explanation:

To find the point on PQ that divides the line segment directed from P to Q into the ratio of 1:3, we can use the concept of the section formula. Let's assume the coordinates of P are (x1, y1) and the coordinates of Q are (x2, y2). Denoting the point dividing PQ by the ratio 1:3 as (x, y), we can use the formula:

x = (x1 + 1/4(x2 - x1))

y = (y1 + 1/4(y2 - y1))

Plugging in the given values, we get:

x = (3/2 + 1/4(8 - 3/2)) = 5/2

y = (5 + 1/4(3 - 5)) = 3

Therefore, the point on PQ that divides the line segment into the ratio of 1:3 is (5/2, 3).