find the coordinates of the point $\frac{1}{3}$ of the way from a to b. coordinates = ( )

Question

Accepted Answer

# Explanation:
## Step1: Calculate the x - coordinate
Use the section formula $x = x_1+\frac{1}{3}(x_2 - x_1)$, where $x_1=-3$, $x_2 = 12$.
$$
\begin{align*}
x&=-3+\frac{1}{3}(12-(-3))\
&=-3+\frac{1}{3}(12 + 3)\
&=-3+\frac{1}{3}\times15\
&=-3 + 5\
&=2
\end{align*}
$$
## Step2: Calculate the y - coordinate
Use the section formula $y = y_1+\frac{1}{3}(y_2 - y_1)$, where $y_1=-2$, $y_2 = 4$.
$$
\begin{align*}
y&=-2+\frac{1}{3}(4-(-2))\
&=-2+\frac{1}{3}(4 + 2)\
&=-2+\frac{1}{3}\times6\
&=-2+2\
&=0
\end{align*}
$$

# Answer:
$(2,0)$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Calculate the x - coordinate

Step2: Calculate the y - coordinate

Answer: