Question

question 7 (multiple choice worth 1 points) (04.03r mc) point b on a segment with endpoints a(2, -2) and c(4, 1) partitions the segment in a 1:3 ratio. find b. (2.5, -1.25) (0.5, 0.75) (-1.25, 2.5) (0.75, 0.5)

Explanation:

Step1: Use the section formula

The section formula for a point \( B(x,y) \) that divides the line segment joining \( A(x_1,y_1) \) and \( C(x_2,y_2) \) in the ratio \( m:n \) is \( x=\frac{mx_2 + nx_1}{m + n} \) and \( y=\frac{my_2+ny_1}{m + n} \). Here \( m = 1 \), \( n = 3 \), \( x_1=2 \), \( y_1=-2 \), \( x_2 = 4 \), \( y_2=1 \).

Step2: Calculate the \( x \) - coordinate of \( B \)

Substitute the values into the \( x \) - coordinate formula:
\( x=\frac{1\times4+3\times2}{1 + 3}=\frac{4 + 6}{4}=\frac{10}{4}=2.5 \)

Step3: Calculate the \( y \) - coordinate of \( B \)

Substitute the values into the \( y \) - coordinate formula:
\( y=\frac{1\times1+3\times(-2)}{1 + 3}=\frac{1-6}{4}=\frac{-5}{4}=-1.25 \)

Answer:

\((2.5,-1.25)\)