Question

Will mark Brainliest!!!!! Suppose A, R, and B are collinear on AB, and

Answer 1

Answer:

$R(x,y) = (\frac{7}{4},\frac{1}{4})$

Step-by-step explanation:

Given

$A = (1,-1)$

$B = (4,4)$

$AR:AB = 1:4$

Required

Determine R

This question will be solved using line ratio formula

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

Where

$A = (1,-1)$

$B = (4,4)$

$m:n = AR : RB$

Since R is on A and B;

$AB = AR + RB$

$4 = 1 + RB$

$RB = 3$

Hence;

$m:n = 1 : 3$

$A = (1,-1)$

$B = (4,4)$

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

$R(x,y) = (\frac{1 * 4 + 3 * 1}{1+3},\frac{1 * 4 + 3 * -1}{1 + 3})$

$R(x,y) = (\frac{4 + 3}{4},\frac{4 - 3}{4})$

$R(x,y) = (\frac{7}{4},\frac{1}{4})$