Question

Point A is at (6,-6) and point C is at (-6,-2). Find the coordinates of point B on line AC such that AB= 3/4 AC Urgent, need this immediately. PLS EXPLAIN

Answer 1

Answer:

$B(x,y) = (-3,0)$

Step-by-step explanation:

Given

$A = (6,-6)$

$C = (-6,2)$

$AB = \frac{3}{4} AC$

Required

Find coordinates of B

First, we need to convert $AB = \frac{3}{4} AC$ to ratio $AB:BC$

SInce $AB = \frac{3}{4} AC$, then

$AB : BC = 3 : 4 - 3$

$AB : BC = 3 : 1$

The coordinates of B can then be calculated as follows;

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

Where

$A(x_1,y_1) = A(6,-6)$

$C(x_2,y_2) = A(-6,2)$

$m:n = 3 : 1$

Substitute these values in the given formula;

$B(x,y) = (\frac{1 * 6 + 3 * -6}{1 + 3},\frac{1 * -6 + 3 * 2}{1 + 3})$

$B(x,y) = (\frac{6 -18}{4},\frac{-6 + 6}{4})$

$B(x,y) = (\frac{-12}{4},\frac{0}{4})$

$B(x,y) = (-3,0)$

Hence, the coordinates of B is $(-3,0)$

Answer 2

(-3,0)..................