Day 4 & Day 5 Bootcamp 8th

Triangle TRW is shown on the coordinate grid. Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R'?

• (−3/n, −5/n)

• (−3n, −5n)

• (−3 + n, −5 + n)

• (−3 − n, −5 − n)

Polygon LMN PQR is shown on the coordinate grid and models the shape of a garden in a park. Polygon LMN PQR will be dilated with the origin as the center of dilation to create polygon L'M'N'P'Q'R'. The vertex Q' will be located at (21, 7). Which rule best represents the dilation?

• (x, y) → (2/7x, 2/7y)

• (x, y) → (x + 15, y + 5)

• (x, y) → (x – 15, y – 5)

• (x, y) → (7/2x, 7/2y)

The table shows the coordinates of the vertices of pentagon ABCDE. Pentagon ABCDE is dilated by a scale factor of (7/3) with the origin as the center of dilation to create pentagon A'B'C'D'E'. If (x, y) represents the location of any point on pentagon ABCDE, which ordered pair represents the location of the corresponding point on pentagon A'B'C'D'E'?

• (3/7)x, (3/7)y

• (x + 7/3, y + 7/3)

• (x + 3/7, y + 3/7)

• (7/3)x, (7/3)y

If (x, y) represents the location of any point on triangle XYZ, which ordered pair represents the location of the corresponding point on triangle X'Y'Z'?

• \(\left(\frac{3}{2}x, \frac{3}{2}y\right)\)

• \(x + \frac{3}{2}, y + \frac{3}{2}\)

• \(\left(\frac{2}{3}x, \frac{2}{3}y\right)\)

• \(x + \frac{2}{3}, y + \frac{2}{3}\)

Circle I was dilated with the origin as the center of dilation to create Circle II. Which rule best represents the dilation applied to Circle I to create Circle II?

• (x, y) → (3/8x, 3/8y)

• (x, y) → (8/3x, 8/3y)

• (x, y) → (x + 5, y + 5)

• (x, y) → (x - 5, y - 5)

The side lengths in yards of a triangle and a square are shown in the diagram. The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?

What is the value of x in the equation represented by the tiles?

• 3

• 5

• -3

• -1

A water heater has a diameter of 18 inches. It sits in a drain pan that has a diameter of 22 inches and a height of 2 inches, as modeled in the diagram below. Water that leaks out of the water heater sits in the drain pan. Which of the following is closest to the maximum amount of water that the drain pan can contain with the water heater in the position shown?

• 13 in³

• 1,005 in³

• 251 in³

• 50 in³

A paper drinking cup in the shape of a cone has a height of 10 centimeters and a diameter of 8 centimeters. Which of the following is closest to the volume of the cup in cubic centimeters?

• 167 cm³

• 209 cm³

• 670 cm³

• 502 cm³

The measures of two angles are (5x + 24)° and (9x - 17)°. What is the value of x if these angles are congruent?

• 1.75

• 13.2

• 0.5

• 10.25