The image of the point (-5, 4) under a translation is (-3,-1). Find the coordinates of the image of the point (-2,9) under the same translation.
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The  coordinates of the image of the point (-2,9) under the same translation will be: (0, 4)

Step-by-step explanation:

Given that the image of the point (-5, 4) under a translation is (-3,-1).

It means the image (-3, -1) is obtained by moving the right side by 2 units and moving 5 units down.

In other words, the rule of translation is:

P(x, y) → (x+2, y-5)

(-5, 4) → (-5+2, 4-5) → (-3, -1)

now

TRANSLATING THE POINT (-2, 9)

We already know the translation rule

P(x, y) → (x+2, y-5)

so

(-2, 9)  → (-2+2, 9-5)  → (0, 4)

Therefore,

The  coordinates of the image of the point (-2,9) under the same translation will be: (0, 4)

what shape is

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