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QuestionFind the coordinate of PP as the weighted average of points: W=−7W = -7 (weight 2), X=−4X = -4 (weight 1), Y=0Y = 0 (weight 3).

Studdy Solution

STEP 1

Assumptions1. Point WW has a coordinate of -7 and a weight of units. Point XX has a coordinate of -4 and a weight of1 unit3. Point YY has a coordinate of0 and a weight of3 units4. The weighted average is calculated by summing the product of each point's coordinate and its weight, then dividing by the total weight.

STEP 2

First, we need to calculate the total weight. This is the sum of the weights of all points.
Total weight=Weight of W+Weight of X+Weight of YTotal\, weight = Weight\, of\, W + Weight\, of\, X + Weight\, of\, Y

STEP 3

Plug in the given values for the weights of the points to calculate the total weight.
Total weight=2+1+3Total\, weight =2 +1 +3

STEP 4

Calculate the total weight.
Total weight=2+1+3=6Total\, weight =2 +1 +3 =6

STEP 5

Now, we need to calculate the sum of the products of each point's coordinate and its weight. This is given by the formulaSum of products=W coordinate×W weight+X coordinate×X weight+Y coordinate×Y weightSum\, of\, products = W\, coordinate \times W\, weight + X\, coordinate \times X\, weight + Y\, coordinate \times Y\, weight

STEP 6

Plug in the given values for the coordinates and weights of the points to calculate the sum of the products.
Sum of products=−×2+−4×1+0×3Sum\, of\, products = - \times2 + -4 \times1 +0 \times3

STEP 7

Calculate the sum of the products.
Sum of products=−7×2+−4×1+0×3=−14−4+0=−18Sum\, of\, products = -7 \times2 + -4 \times1 +0 \times3 = -14 -4 +0 = -18

STEP 8

Now that we have the sum of the products and the total weight, we can calculate the coordinate of thatrepresentstheweightedaverage.Thisisgivenbytheformula that represents the weighted average. This is given by the formula\, coordinate = Sum\, of\, products / Total\, weight$$

STEP 9

Plug in the values for the sum of the products and the total weight to calculate the coordinate of $$.
 coordinate=−18/6\, coordinate = -18 /6

STEP 10

Calculate the coordinate of $$.
 coordinate=−18/6=−3\, coordinate = -18 /6 = -3The coordinate of $$ that represents the weighted average of the set of points is -3.

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