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QuestionFind the coordinate of PP as the weighted average of points BB and DD, where BB at -6 weighs 3 times DD at 2.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point B and D are -6 and respectively. . Point B weighs three times as much as point D.
3. We are to find the coordinate of point that represents the weighted average of points B and D.

STEP 2

The weighted average, , of two points, $B$ and , is given by the formula=wB⋅B+wD⋅DwB+wD = \frac{w_B \cdot B + w_D \cdot D}{w_B + w_D}where wBw_B and wDw_D are the weights of points B and D respectively.

STEP 3

Given that point B weighs three times as much as point D, we can denote the weight of point D as wD=1w_D =1 and the weight of point B as wB=3w_B =3.

STEP 4

Now, plug in the given values for the weights and coordinates of points B and D into the formula for the weighted average.
=3⋅(−6)+1⋅23+1 = \frac{3 \cdot (-6) +1 \cdot2}{3 +1}

STEP 5

implify the numerator of the fraction.
=−18+24 = \frac{-18 +2}{4}

STEP 6

Further simplify the numerator of the fraction.
=−164 = \frac{-16}{4}

STEP 7

Finally, divide the numerator by the denominator to find the coordinate of point.
=−16/4=−4 = -16 /4 = -4The coordinate of point that represents the weighted average of points B and D is -4.

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