Question

A,b, and c.are collinear and b is between a and c the ratio of ab to bc is 3:1 if a is at (-2-8) and b is at (1,1) what are the coordinates of c

Answer 1

Step-by-step explanation:

To find the coordinates of C,If A,B, and C are collinear and b is between a and c the ratio of ab to bc is 3:1 if a is at (-2-8) and b is at (1,1).

A--------- 3-------B -----1--------- C

.______________._____________.

(-2,-8)-------- (1,1) ---------- (x,y)

Section Formula:

If two points (x1,y1) and (x2,y2) are divided by the third point (x,y) in the ratio m:n,then the coordinates of third point

$x = \frac{mx_2 + nx_1}{m + n} \\ \\ y = \frac{my_2 + ny_1}{m + n}$

here A(x1,y1) B(x,y) and C(x2,y2)

m:n=3:1

$1 = \frac{3x + 1.( - 2)}{3 + 1} \\ \\ 4 = 3x - 2 \\ \\ 3x = 4 + 2 = 6 \\ \\ x = \frac{6}{3} \\ \\ x = 2\\ \\ 1 = \frac{3y + 1( - 8)}{3 + 1} \\ \\ 4 = 3y - 8 \\ \\ 3y = 4 + 8 \\ \\ 3y = 12 \\ \\ y = \frac{12}{3} \\ \\ y = 4$

Thus coordinates of C are (2,4).

Hope it helps you.

Answer 2

Answer:

coordinates of C are (2,4).