Question

What are the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that the ratio of ABABA, B to BCBCB, C is 2:32:32, colon, 3?

A) 2 1/5, 1/5
B) 2 1/4, 1/4
C) 3 3/4, 3/4
D) 3 3/5, 3/5

Answer 1

A) 2 1/5, 1/5

Explanation:

A) 2 1/5, 1/5

ratio is- 2/3

m/n is ratio

so

m=2

n=3

mx(2) + nx(1) / m+n = x coordinate

my(2) + my(1)/m+n= y coordinate

you get 2 1/5 and 1/5

Answer 2

The coordinates of point B on line segment AC such that AB/BC = 2/3 are (2 1/4, 1/4). The correct answer is B).

Let A = (0, 0) and C = (5, 0). We are given that the ratio of AB to BC is 2:3. This means that point B divides segment AC in the ratio 2:3.

Using the section formula, we can find the coordinates of point B:

x_B = (2x_C + 3x_A) / (2 + 3) = (2(5) + 3(0)) / (2 + 3) = 10/5 = 2

y_B = (2y_C + 3y_A) / (2 + 3) = (2(0) + 3(0)) / (2 + 3) = 0/5 = 0

Therefore, the coordinates of point B are (2, 0), which is equivalent to 2 1/4, 1/4. The correct answer is B) 2 1/4, 1/4.