8th Grade Math Test, Mod 2

• Triangle DEF has vertices at D(-3, -1), E(1,8), F(5, -1).

• Triangle DEF has vertices at D(20, -4), E(4, 32), F(-12, -4).

• Triangle DEF has vertices at D(-12, -4), E(4, 32), F(20, -4).

• Triangle DEF has vertices at D(1, 3), E(5, 12), F(9, 3).

Rectangle WXYZ is rotated 90º around the origin and then dilated by a scale factor of ⅙ centered at (0, 0) to produce rectangle LMNO. Select all true statements about rectangles WXYZ and LMNO.

• LMNO has a smaller area than WXYZ.

• The rectangles are congruent.

• The rectangles are similar.

• The perimeters of the rectangles are the same.

• WXYZ and LMNO have different angles.

Answer explanation

Dilating a shape makes the resulting shape similar, but not congruent. In other words, all of their proportions and angles are the same, but they are not the same size.

Mathematical Equivalence

ON

Triangle QRS has a perimeter of 42 units. It is dilated by a scale factor of ⅙ centered at (0, 0) and then translated 2 units to the left to produce triangle TUV. What is the perimeter of triangle TUV?

Mathematical Equivalence

ON

Answer explanation

Since each side of ABC is scaled down by a factor of ⅙, the perimeter is also proportionally scaled down by ⅙ from 42 to 7 units. The translation does not affect the perimeter of TUV. So the perimeter of TUV is 7 units.

Dilate parallelogram BCDE by a scale factor of 3 centered at (-2, 1) and then graph the vertices of the image.

Answer explanation

To find a dilation centered at a point not at the origin, we must first subtract the x and y of the center of dilation from the x and y of each original point. Next, we must multiply this difference for each point by the scale factor. Finally, we can add this product to the center of dilation to find the new x and y for each point.

Triangle GHI with vertices G(0, 6), H(-4, 3), I(2, 2) is mapped to an image G'H'I' with vertices G'(0, 20), H'(-20,5), and I'(10, 0). What rule was used to map this image?

Answer explanation

Take each vertex and plug it into the rule to find which one fits the image.

Triangle GHI with vertices G(0, 6), H(-4, 3), I(2, 2) is mapped to an image G'H'I' with vertices G'(0, 20), H'(-20,5), and I'(10, 0). Describe the sequence of transformations that map GHI to G'H'I'.

Answer explanation

First, each point in GHI is shifted down by 2 units. Then, each point is dilated by a scale factor of 5 centered at the origin.

Geometry is good for everyone to know, especially artists. Draw a picture using only triangles and quadrilaterals.

Triangle ABC has side lengths of 5 in, 4 in, and 3 in. Triangle DEF has side lengths 10 in, 16 in, 21 in. Are these triangles similar? Explain why or why not.

Answer explanation

These triangles are not similar since their side lengths are not all proportional to each other.

Trapezoid MNOP has an area of 57 m². Which area could represent a dilation of MNOP? Select all that apply.

• 18 m²

• 3 m²

• 19 m²

• 114 m²

Answer explanation

57 m² can be dilated by any number, even decimal numbers, so every area is could potentially be the area of the image of MNOP.