Question

1. line segment cd has endpoints at c(7, -4) and d(-5, 4).

we want to find the coordinates of point p so that p partitions cd into a ratio of 3
to 1.
b. fill in the correct values for the formula below:
p = ( + ( -
), + (
-
)

Explanation:

Step1: Recall the section formula

The section formula for a point \(P(x,y)\) that divides the line segment joining \(C(x_1,y_1)\) and \(D(x_2,y_2)\) in the ratio \(m:n\) is \(P=(x_1+\frac{m}{m + n}(x_2 - x_1),y_1+\frac{m}{m + n}(y_2 - y_1))\). Here \(x_1 = 7,y_1=-4,x_2=-5,y_2 = 4,m = 3,n = 1\).

Step2: Substitute the values into the formula

For the \(x\) - coordinate: \(x=7+\frac{3}{3 + 1}(-5 - 7)\). For the \(y\) - coordinate: \(y=-4+\frac{3}{3 + 1}(4-(-4))\).

Answer:

\(P=(7+\frac{3}{4}(-5 - 7),-4+\frac{3}{4}(4-(-4)))\)