Question

Given points A(-4,7) and B(12,-1), what are the coordinates of point C on AB, so that C partitions AB in the ratio 1 to 7?

A) (-2,6)
B) (-2,7)
C) (-2,5)
D) (2,-6)

Answer 1

The coordinates of point C that partitions the segment AB in the ratio 1 to 7 are (-2,6), which is option A using the section formula for internal division.

Step-by-step explanation:

To find the coordinates of point C that partitions the segment AB in the ratio 1 to 7, we can use the section formula for internal division. The coordinates of A are (-4,7) and B are (12,-1). We'll represent the coordinates of C as (x,y) and apply the formula:

(x,y) = ((m * x2 + n * x1) / (m + n), (m * y2 + n * y1) / (m + n))

Here, m=1 and n=7 (given ratio), x1=-4, y1=7 (coordinates of A), and x2=12, y2=-1 (coordinates of B). Substituting these values:

(x,y) = ((1*12 + 7*(-4)) / (1 + 7), (1*(-1) + 7*7) / (1 + 7))

(x,y) = ((12 - 28) / 8, (-1 + 49) / 8)

(x,y) = (-16 / 8, 48 / 8)

(x,y) = (-2, 6)

Therefore, the coordinates of point C are (-2, 6), which corresponds to option A.