Question

Given the points M(-3,-4) and T(7.1), find the coordinates of the point Q on a directed line segment MT that partitions segment MT in the ratio of 2:3.

a) (-1.2, -1.6)
b) (-0.5, -2)
c) (0.3, -2.8)
d) (1.7, -3.4)

Answer 1

The coordinates of point Q that partitions the segment MT in the ratio 2:3 are (1, -2), found using the section formula for internal division.

Step-by-step explanation:

To find the coordinates of the point Q that partitions the segment MT in the ratio 2:3, we can use the section formula. Since the ratio is 2:3, we can label the parts as 2k and 3k, respectively, with the total being 5k. So, point Q will divide the line into 2 parts in such a way that MQ: QT = 2:3. Using the formula for internal division,

• Qx = (m * Tx + n * Mx) / (m + n)
• Qy = (m * Ty + n * My) / (m + n)

where M(-3, -4), T(7, 1), m=2, and n=3. Inserting these values into the formula, we get:

Qx = (2 * 7 + 3 * (-3)) / (2 + 3) = (14 - 9) / 5 = 5 / 5 = 1

Qy = (2 * 1 + 3 * (-4)) / (2 + 3) = (2 - 12) / 5 = -10 / 5 = -2

Therefore, the coordinates of point Q are (1, -2), which corresponds to option (b).