Question

Segment CD is shown on the graph. Which shows how to find the y-coordinate of the point that will divide CD into a 5:2 ratio

Answer 1

Answer:

C. y=[5/7](3-1)+1

Explanation:

Segment CD is shown on the graph. Which shows how to find the y-coordinate of the point that will divide CD into a 5:2 ratio

A. y=[5/2](3-1)+1

B. y=[5/2](3+4)-4

C. y=[5/7](3-1)+1

D. y=[5/7](3+4)-4

The coordinates of point C is (-4,1) and the coordinate of point D is (3,3)

The formula for dividing a line XY in ratio a:b, with point X at (x₁, y₁) and Y at (x₂, y₂) is given by the equation:

$y=\frac{a}{a+b} (y_2-y_1)+y_1$

Point C is (-4,1) = (x₁, y₁), therefore x₁ = -4 and y₁ = 1. point D is (3,3), therefore x₂, = 3 and y₂ = 3.

The ratio = 5:2, therefore a= 5 and b = 2.

Substituting into the formula gives:

$y=\frac{a}{a+b} (y_2-y_1)+y_1\\y=\frac{5}{5+2} (3-(1))+(1)\\y=\frac{5}{7} (3-1)+1$