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:
[tex]y=\frac{a}{a+b} (y_2-y_1)+y_1[/tex]
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:
[tex]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[/tex]
