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QuestionFind point PP as the weighted average of points WW, XX, and YY where W=−7W=-7, X=−4X=-4, Y=0Y=0 with weights 2, 1, and 3.

Studdy Solution

STEP 1

Assumptions1. The coordinates of points WW, XX, and YY are −7-7, −4-4, and 00 respectively. . The weight of point WW is twice that of point XX.
3. The weight of point YY is three times that of point XX.
4. The weight of point XX is 11 (this is an arbitrary choice that simplifies calculations, as the relative weights are what matter).

STEP 2

Given the weights of the points, we can assign the weights as followsWeightW=2∗WeightX=2Weight_W =2 * Weight_X =2
WeightX=1Weight_X =1
WeightY=∗WeightX=Weight_Y = * Weight_X =

STEP 3

The weighted average of a set of numbers is calculated by multiplying each number by its weight, summing these products, and then dividing by the sum of the weights.=WeightW∗CoordinateW+WeightX∗CoordinateX+WeightY∗CoordinateYWeightW+WeightX+WeightY = \frac{Weight_W * Coordinate_W + Weight_X * Coordinate_X + Weight_Y * Coordinate_Y}{Weight_W + Weight_X + Weight_Y}

STEP 4

Substitute the given values into the formula.
=2∗−7+1∗−4+3∗02+1+3 = \frac{2 * -7 +1 * -4 +3 *0}{2 +1 +3}

STEP 5

Perform the multiplication in the numerator and the addition in the denominator.
=−14−4+0 = \frac{-14 -4 +0}{}

STEP 6

Perform the addition in the numerator.
=−186 = \frac{-18}{6}

STEP 7

Divide the numerator by the denominator to find the coordinate of point $$.
=−3 = -3So, the coordinate of point $$ that represents the weighted average of the set of points $W$, $X$, and $Y$ is $-3$.

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