c#6 find the coordinates of the point $\frac{3}{4}$ of the way from $a(7,-5)$ to $b(-9,3)$.
c#7 the angles $angle ghi$ and $angle jhk$ are vertical to each other. knowing that $mangle ghi=(5x + 13)^{circ}$ and $mangle jhk=(7x - 21)^{circ}$: sketch a picture of the situation, solve for $x$, and find $mangle ghi$.

Question

Accepted Answer

# Explanation:
## Step1: Use the section formula
The section formula for 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 $m:n$ is given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 3$, $n=1$, $x_1 = 7$, $y_1=-5$, $x_2=-9$, $y_2 = 3$.
## Step2: Calculate the $x$ - coordinate
Substitute the values into the $x$ - coordinate formula:
$$
\begin{align*}
x&=\frac{3\times(-9)+1\times7}{3 + 1}\
&=\frac{-27 + 7}{4}\
&=\frac{-20}{4}\
&=-5
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate
Substitute the values into the $y$ - coordinate formula:
$$
\begin{align*}
y&=\frac{3\times3+1\times(-5)}{3 + 1}\
&=\frac{9-5}{4}\
&=\frac{4}{4}\
&=1
\end{align*}
$$

# Answer:
The coordinates of the point are $(-5,1)$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the section formula

Step2: Calculate the \(x\) - coordinate

Step3: Calculate the \(y\) - coordinate

Answer: