Question

In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? A. (2, -1) B. (5, -3) C. (2, -3) D. (7, -1)

Answer 1

Answer:

A.

$Point\ C = (2,-1)$

Step-by-step explanation:

Given

$A = (2,-6)$

$B = (10,2)$

$m:n = 5:3$

Required

Determine the coordinates of C

Since, point D divides line AB in ratio, 5 : 3;

We start by calculating the coordinates of D;

This is done as follows;

$D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

$(x_1,y_1) = (2,6)$

$(x_2,y_2) = (10,2)$

$m:n = 5:3$

$D(x,y) = (\frac{5 * 10 + 3 * 2}{5+3},\frac{5 * 2 + 3 * -6}{5+3})$

$D(x,y) = (\frac{50 + 6}{8},\frac{10 - 18}{8})$

$D(x,y) = (\frac{56}{8},\frac{-8}{8})$

$D(x,y) = (7},-1)$

Since AC is vertical

Then, Point C has the same x coordinate as A

$x-coordinate = 2$

Similarly;

Since CD is horizontal

Then, Point C has the same y coordinate as D

$y-coordinate = -1$

Hence,

$Point\ C = (2,-1)$