Question

find the coordinates of p that represent the weighted av

• a has a weight of 3.
• b has a weight of 1.

a(-1, -7)
b(4, 8)

Explanation:

Step1: Recall weighted - average formula for x - coordinate

The formula for the x - coordinate of the weighted average of two points $(x_1,y_1)$ and $(x_2,y_2)$ with weights $w_1$ and $w_2$ is $x=\frac{w_1x_1 + w_2x_2}{w_1 + w_2}$. Here, $A(-1,-7)$ with $w_1 = 3$, $B(4,8)$ with $w_2=1$, and we first find the x - coordinate of $P$.
$x=\frac{3\times(-1)+1\times4}{3 + 1}$

Step2: Calculate the x - coordinate

$x=\frac{-3 + 4}{4}=\frac{1}{4}=0.25$

Step3: Recall weighted - average formula for y - coordinate

The formula for the y - coordinate of the weighted average of two points $(x_1,y_1)$ and $(x_2,y_2)$ with weights $w_1$ and $w_2$ is $y=\frac{w_1y_1+w_2y_2}{w_1 + w_2}$.
$y=\frac{3\times(-7)+1\times8}{3 + 1}$

Step4: Calculate the y - coordinate

$y=\frac{-21 + 8}{4}=\frac{-13}{4}=-3.25$

Answer:

$(0.25,-3.25)$