Question

find the coordinates of p that represent the weighted average of points a and b below. point a has a weight of \\( \frac { 2 } { 5 } \\). point b has a weight of \\( \frac { 3 } { 5 } \\).

Explanation:

Step1: Find the coordinates of \(A\) and \(B\)

From the graph, \(A=( - 2,6)\) and \(B=(5,1)\)

Step2: Use the weighted - average formula for coordinates

The formula for the \(x\) - coordinate of the weighted average \(x_P\) is \(x_P = w_Ax_A+w_Bx_B\), and for the \(y\) - coordinate \(y_P = w_Ay_A + w_By_B\), where \(w_A=\frac{2}{5}\), \(w_B=\frac{3}{5}\), \(x_A=-2\), \(y_A = 6\), \(x_B = 5\), \(y_B=1\)

For the \(x\) - coordinate:

$$
LATEXBLOCK0
$$

For the \(y\) - coordinate:

$$
LATEXBLOCK1
$$

Answer:

The coordinates of \(P\) are \((2.2,3)\)