Answer:
D.) (-1, 1), (-1, 5), (-7, 1)
Explanation:
The length of the horizontal segment of the triangle graphed is 3. The length of the vertical segment of the triangle graphed is 2. Using the Pythagorean theorem, this makes the length of the missing side
2²+3²=c²
4+9 = c²
13=c²
√13 = c
This makes our side lengths 2, 3, and √13.
For choice A our vertices are (-1, 1), (-1, 4), (-6, 1).
This makes the length of the horizontal segment 5 and the length of the vertical segment 3. This makes the missing side length
5²+3²=c²
25+9=c²
34=c²
√34 = c
This is not proportional to the triangle drawn, so it is not similar.
The vertices of the triangle in option B 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
4²+5²=c²
16+25=c²
41=c²
√41=c
These are not proportional to the triangle drawn, so the triangles are not similar.
The vertices of the triangle in choice C 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
3²+6²=c²
9+36=c²
45=c²
√45=c
3√5=c
These sides are not proportional to the sides of the triangle drawn, so the triangles are not similar.
The vertices of the triangle in choice D 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
6²+4²=c²
36+16=c²
52=c²
√52=c²
2√13=c
These sides are all twice as long as the sides of the triangle drawn; this means the triangles are similar.