Point A(2, 5) is dilated from the origin with scale factor 3 , resulting in point A′ . Darius says the coordinates of point A′ are (6, 15) . Marcia says the coordinates of point A′ are (4, 13) . Who is correct?

It actually doesn't matter! The key thing is that the dilation value affects the distance between two points. As in the first example (dilation by a factor of 3), A is originally 1 unit down from P and 2 units to the left of P.

1*3 = 3, so A' (the dilated point) should be 3 units down from P.

2*3 = 6, so A' should be 6 units to the left of P.

It doesn't matter if you go left first or down first, because you always determine the location of A' with respect to P based on the location of A (which doesn't move) with respect to P.

Step-by-step explanation:

step-by-step explanation:

|ab| = 1.4 = 4

h = 1.4 = 4

a(abc) area = 4.4 = 16/2 = 8

area of abc = 8 cm^2

good luck ! ; )

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.