Yuron is sketching a scale drawing of a famous painting. The painting is 54 inches wide and 72 inches long. He used a scale factor of Two-thirds to make his sketch. How many inches wide is Yuron's sketch? 36 48 81 84

36 inches

Step-by-step explanation:

From the information given in the question, we are informed that Yuron is sketching a scale drawing of a famous painting and that the painting is 54 inches wide and 72 inches long.

We are further informed that he used a scale factor of ⅔ to make his sketch, then the measure of the width of the sketch will be ⅔ of the original width and this will be:

= ⅔ × 54 inches

= 36 inches

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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