line segment pr is a directed line segment beginning at p(-10,7) and ending at r(8,-5). find point q on the line segment pr that partitions it into the segments pq and qr in the ratio 4:5. a. (-2, -5/3) b. (-2, 5/3) c. (0, -1/3) d. (-9/2, 3)

Question

Accepted Answer

# Explanation:
## Step1: Use the section formula
If a point $Q(x,y)$ divides the line segment joining $P(x_1,y_1)$ and $R(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2 + nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here $x_1=-10,y_1 = 7,x_2 = 8,y_2=-5,m = 4,n = 5$.
## Step2: Calculate the $x$ - coordinate of $Q$
Substitute the values into the $x$ - formula:
$$
\begin{align*}
x&=\frac{4\times8+5\times(-10)}{4 + 5}\
&=\frac{32-50}{9}\
&=\frac{-18}{9}\
&=- 2
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $Q$
Substitute the values into the $y$ - formula:
$$
\begin{align*}
y&=\frac{4\times(-5)+5\times7}{4 + 5}\
&=\frac{-20 + 35}{9}\
&=\frac{15}{9}\
&=\frac{5}{3}
\end{align*}
$$

# Answer:
B. $(-2,\frac{5}{3})$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the section formula

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

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

Answer: