point q lies on the segment $ \overline { p r } $
he coordinates of q so that the ratio of pq to qr is 2 to 5.

Question

Accepted Answer

# Explanation:
## Step1: Use the section formula
The section formula for a point $Q(x,y)$ that divides the line segment joining $P(x_1,y_1)$ and $R(x_2,y_2)$ in the ratio $m:n$ is given by $x=\frac{mx_2 + nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 2$, $n = 5$, $x_1=-29$, $y_1=-12$, $x_2 = 6$, $y_2=2$.
## Step2: Calculate the $x$ - coordinate of $Q$
Substitute the values into the $x$ - coordinate formula:
$$
\begin{align*}
x&=\frac{2\times6+5\times(-29)}{2 + 5}\
&=\frac{12-145}{7}\
&=\frac{-133}{7}\
&=-19
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $Q$
Substitute the values into the $y$ - coordinate formula:
$$
\begin{align*}
y&=\frac{2\times2+5\times(-12)}{2 + 5}\
&=\frac{4-60}{7}\
&=\frac{-56}{7}\
&=-8
\end{align*}
$$

# Answer:
$(-19,-8)$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Use the section formula

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

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

Answer: