Triangle BCD has vertices B(-8, 3), C(-4, 6), and D(2,0). If the triangle is reflected across the x-axis and dilated by a scale factor of 0.5 with respect to the origin, what are the coordinates of the vertices of triangle B'C'D'?

A. B'(-4, 1.5), C'(-2,-3), D'(1, 0)
B. B'(-8, 3), C (-4,-6), D (2,0)
C. B*(-4,2), C (-2,-3), D'(1, 0)
D. B(-16, 6), C'(-8, -12), D'(4,0)

B'(-4, 1.5), C'(-2,-3), D'(1, 0)

Step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt