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QuestionFind coordinates of PP as the weighted average of U(−8,−5)U(-8,-5) and X(2,0)X(2,0), with UU weighing twice as much as XX.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point U are (-8,-5) . The coordinates of point X are (,0)
3. Point U weighs twice as much as point X4. We are finding the weighted average of these points

STEP 2

The weighted average of two points is given by the formula=w1⋅U+w2⋅Xw1+w2 = \frac{w1 \cdot U + w2 \cdot X}{w1 + w2}where w1w1 and w2w2 are the weights of points U and X respectively.

STEP 3

Given that point U weighs twice as much as point X, we can set w1=2w1 =2 and w2=1w2 =1.

STEP 4

Now, we can plug in the given values for the coordinates of points U and X, and their weights into the formula.
=2⋅(−8,−)+1⋅(2,0)2+1 = \frac{2 \cdot (-8,-) +1 \cdot (2,0)}{2 +1}

STEP 5

Perform the multiplication in the numerator.
=(−16,−10)+(2,0)3 = \frac{(-16,-10) + (2,0)}{3}

STEP 6

Add the vectors in the numerator.
=(−14,−10)3 = \frac{(-14,-10)}{3}

STEP 7

Divide each coordinate by the denominator to find the coordinates of point.
=(−14/3,−10/3) = (-14/3, -10/3)So, the coordinates of point that represent the weighted average of points U and X are (−14/3,−10/3)(-14/3, -10/3).

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