Which triangle defined by the given points on the coordinate plane is similar to the triangle illustrated?

The correct option in the attached image is:

D. (-1, 1), (-1, 5), (-7, 1)

Step-by-step explanation:

Please refer to the attached image.

The length of the horizontal segment of the graphed triangle is 3.  The length of the vertical segment of the triangle graphed is 2. We will use the Pythagorean theorem to find the length of the missing side thus:

x² = 2²+3²

x² = 4+9

x² = 13

x = √13 or 3.6

This makes our side lengths 2, 3, and 3.6

For option A, our vertices are (-1, 1), (-1, 4), (-6, 1). This means the length of the horizontal segment 5 and the length of the vertical segment 3.  This missing side length is calculated thus:

x² = 5²+3²

x² = 25+9

x² = 34

x = √34 or 5.83

This is not proportional to the triangle drawn, so it is not similar.

For option B, our vertices are (-1, 1), (-1, 5), and (-6, 1).  This makes the horizontal segment 5 units long and the vertical segment 4 units long.  This makes the missing side length

x² = 4²+5²

x² = 16+25

x² = 41

x = √41 or 6.4

These are not proportional to the triangle drawn, so the triangles are not similar.

For option C, our vertices are (-1, 1), (-1, 4) and (-7, 1).  This makes the length of the horizontal segment 6 and the length of the vertical segment 3.  This makes the missing side length

x² = 3²+6²

x² = 9+36

x² = 45

x = √45 or 3√5 or 6.7

These sides are not proportional to the sides of the triangle drawn, so the triangles are not similar.

For option D, our vertices are (-1, 1), (-1, 5) and (-7, 1).  This makes the length of the horizontal segment 6 and the length of the vertical segment 4.  This makes the missing side length

x² = 6²+4²

x² = 36+16

x² = 52

x = √52 or 2√13 or 7.21

These sides are all twice as long as the sides of the triangle drawn, this indicates that the triangles are similar. Therefore our answer is D.

step-by-step explanation:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.