8th Grade Fourth Six Weeks Test

An architect places his building model that is 2.5 feet tall on the ground 2 feet away from point M. A line segment drawn from the top corner of the actual building to point M creates two similar triangles.

Which proportion can be used to find h, the height of the actual building in feet?

• $A\ \ \ \ \ \frac{2}{2.5}\ =\ \frac{21}{h}$

• $B\ \ \ \ \ \frac{2}{19}\ =\ \frac{h}{2.5}$

• $C\ \ \ \ \ \frac{2}{2.5}\ =\ \frac{h}{21}$

• $D\ \ \ \ \ \frac{2}{h}\ =\ \frac{21}{2.5}$

Triangle ABC is similar to Triangle ADE.

Which of these is x, the distance from Point B to Point C?

• A 20 feet

• B 30 feet

• C 45 feet

• D 53 feet

Q 3. The graphic shows quadrilateral ABCD and its dilation, quadrilateral A prime B prime C prime D prime, with the origin as the center of dilation. The scale factor is 3/4.

• A Quadrilateral ABCD is congruent to quadrilateral A prime B prime C prime D prime.

• B The corresponding angles of quadrilaterals ABCD and A prime B prime C prime D prime are congruent.

• C The corresponding sides of quadrilaterals ABCD and A prime B prime C prime D prime are congruent.

• D The corresponding angles of quadrilaterals ABCD and A prime B prime C prime D prime are not congruent.

Q 4. Triangle ABC has vertices A at (2,3), B at (4,5), and C at (6,1).

If Triangle ABC is dilated by a scale factor of 3/2 and has the origin as the center of dilation, what are the coordinates of B prime?

• A B prime at (3, 4.5)

• B B prime at (6, 15/2)

• C B prime at (9, 3/2)

• D B prime at (5 and 1/2, 6 and 1/2)

Q 5. Using the origin as the center of dilation, Triangle ABC was dilated to create Triangle GHI. Both triangles are represented below.

Which rule best represents the effect of this dilation on the coordinates of triangle ABC?

• A (x, y) goes to (4/5 x, 4/5 y)

• B (x, y) goes to (x plus 2/5, y minus 1)

• C (x, y) goes to x plus 4/5 x, y plus 4/5)

• D (x, y) goes to 5/4 x, 5/4 y)

Q 6. The origin was used as the center of dilation to dilate quadrilateral ABCD as shown.

Which algebraic representation best describes the dilation that was applied to quadrilateral ABCD to create quadrilateral A prime B prime C prime D prime?

• A (x, y) goes to (x plus 3, y plus 3)

• B (x,y) goes to (1.5 x, 1.5 y)

• C (x, y) goes to (2 x, 2 y)

• D (x, y) goes to (2/3 x, 2/3 y)

Q 7. A rectangle has vertices E at ( negative 4, 8), F at (2, 8), G at (2, negative 2) and H at (negative 4, negative 2). The rectangle is dilated so that G prime is located at (5, negative 5). Which algebraic representation represents this dilation?

• A (x, y) goes to (5/2 x, 5/2 y)

• B (5/2 x, 5/2 y) goes to (x, y)

• C (5/2 x, y) goes to (x, 5/2 y)

• D (x, 5/2 y) goes to (5/2 x, y)

Triangle STU is graphed on the coordinate plane as shown.

If triangle STU is rotated 90 degrees counterclockwise about the origin to create triangle S prime T prime U prime, which statement about the figures would be true?

• A The orientation of the figure will be the same, and the figures will be congruent.

• B The orientation of the figure will not be the same.

• C The figures will not be congruent.

• D Both the orientation of the vertices and the orientation of the figure will be the same.

Q 9. Triangle XYZ is translated so that X is mapped to X prime. Which coordinate pairs best represent Y prime and Z prime?

• A y prime (negative 3, negative 8); Z prime (2, negative 3)

• B y prime (2, negative 6); Z prime (negative 3, negative 8)

• C y prime (2, negative 3); Z prime (negative 3, negative 8)

• D y prime (2, negative 3); Z prime (negative 3, negative 4)

Given a parallelogram, which of the following would not result in a parallelogram congruent to the original?

• A Reflecting the parallelogram over the line y equals x.

• B Rotating the parallelogram 90 degrees.

• C Translating the parallelogram 5 units up and 2 units to the left.

• D Dilating the parallelogram by a scale factor of 1/2.