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.
c. what are the coordinates of point p?

Explanation:

Step1: Use 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 \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 7,y_1=-4,x_2=-5,y_2 = 4,m = 3,n = 1\).

Step2: Calculate the \(x\) - coordinate

Substitute the values into the \(x\) - coordinate formula:
\(x=\frac{3\times(-5)+1\times7}{3 + 1}=\frac{-15 + 7}{4}=\frac{-8}{4}=-2\)

Step3: Calculate the \(y\) - coordinate

Substitute the values into the \(y\) - coordinate formula:
\(y=\frac{3\times4+1\times(-4)}{3 + 1}=\frac{12-4}{4}=\frac{8}{4}=2\)

Answer:

The coordinates of point \(P\) are \((-2,2)\)