Question

find the coordinate of the point p that represents the weighted - average for a set of points with the given conditions. point a has a weight of 3/4 and point b has a weight of 1/4. the coordinate of point p is . previous

Explanation:

Step1: Recall weighted - average formula

The formula for the weighted average of two points $x_1$ and $x_2$ with weights $w_1$ and $w_2$ is $x=\frac{w_1x_1 + w_2x_2}{w_1 + w_2}$. Here, $x_1=-9$ (co - ordinate of point A), $w_1=\frac{3}{4}$, $x_2 = 2$ (co - ordinate of point B), and $w_2=\frac{1}{4}$.

Step2: Calculate the numerator

$w_1x_1+w_2x_2=\frac{3}{4}\times(-9)+\frac{1}{4}\times2=\frac{-27 + 2}{4}=\frac{-25}{4}$.

Step3: Calculate the denominator

$w_1 + w_2=\frac{3}{4}+\frac{1}{4}=1$.

Step4: Find the weighted average

$x=\frac{\frac{-25}{4}}{1}=-\frac{25}{4}=- 6.25$.

Answer:

$-6.25$