Question

Consider the line segment pq with endpoints p(-3, -2) and q(2, 3). Which point divides the line segment directed from q to p in the ratio of 3:2?

1) a (-2, -1)
2) (-1, 0)
3) (0, 1)
4) (1, 2)

Answer 1

The point that divides the line segment directed from q to p in the ratio of 3:2 is (-2/5, -1/5).

Step-by-step explanation:

To find the point that divides the line segment directed from q to p in the ratio of 3:2, we can use the section formula. The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m:n, then the coordinates of P are given by:

x = (n * A.x + m * B.x) / (m + n)

y = (n * A.y + m * B.y) / (m + n)

In this case, A and B are the coordinates of q(-3, -2) and p(2, 3) respectively, and m:n is 3:2. Plugging in the values, we get:

x = (2 * -3 + 3 * 2) / (3 + 2) = -2/5

y = (2 * -2 + 3 * 3) / (3 + 2) = -1/5

Therefore, the point that divides the line segment directed from q to p in the ratio of 3:2 is (-2/5, -1/5).