Question

Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2. A. (-5, -15) B. (-23, -5) C. (-13, -7) D. (-11.5, -2.5)

Answer 1

C. (-13, -7)

Explanation:

The location of a point O(x, y) that divides a line AB with location A
`(x_1,y_1)` and B
`(x_2,y_2)` in the ratio m:n is given by:

`x=(m)/(m+n) (x_2-x_1)+x_1\\\\y=(m)/(m+n) (y_2-y_1)+y_1`

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

`x=(5)/(5+2) (-15-(-8))+(-8)\\\\x=(5)/(7) (-15+8)-8=(5)/(7)(-7)-8=-5-8=-13 \\\\\\y=(5)/(5+2) (-13-8)+8\\\\y=(5)/(7) (-21)+8=5(-3)+8=-15+8=-7`

Therefore the coordinates of point X is at (-13, -7)