8. given ab with a(8, - 4) and b(-6, -11), if p partitions ab such that the ratio of ap to ab is 2:7, find the coordinates of p.

Question

Accepted Answer

# Explanation:
## Step1: Recall the section - formula
The coordinates of a point $P(x,y)$ that divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $A(8,-4)$, $B(-6,-11)$, and the ratio $m:n = 2:7$.
## Step2: Calculate the $x$ - coordinate of $P$
$$
\begin{align*}
x&=\frac{2\times(-6)+7\times8}{2 + 7}\
&=\frac{-12 + 56}{9}\
&=\frac{44}{9}
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $P$
$$
\begin{align*}
y&=\frac{2\times(-11)+7\times(-4)}{2 + 7}\
&=\frac{-22-28}{9}\
&=\frac{-50}{9}
\end{align*}
$$

# Answer:
$P(\frac{44}{9},-\frac{50}{9})$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

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

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

Answer: