Geometry and Spatial Reasoning

1. Geometry and Spatial Reasoning Grade 8 TAKS Objective 3

2. Objective 3 • The drawing below shows a solid figure built with cubes. How many cubes can be seen from the top view of the figure? • 8 • 6 • 7 • 9

3. Objective 3 • Which ordered pair names a point that is definitely NOT on the line? • (6, -8) • (-11, -11) • (5, 5) • All the above

4. Objective 3 • Square ABCD was dilated to form square PQRS. Which number best represents the scale factor used to change square ABCD to square PQRS? • 1/4 • 1/5 • 1/7 • 1/8 A B P Q S 5 in R D 25 in C

5. Objective 3 • The square of the diagonal of a square is 54 cm2 . What is the length of the side of the square? • 2√3 cm • 3√2 cm • 3√3 cm • 3√5 cm

6. Objective 3 • A Circle with a radius of 3 units has its center at (-4, -2) on the coordinate grid. If the radius is translated 5 units to the right and 2 units up, what will be the coordinates of the new center? • (2,0) • (1,0) • (0,4) • (5,0)

7. Objective 3 • If ∆ABC is translated 3 units to the right and 3 units down. What will be the coordinates of the vertex C of the translated triangle? • (5, -8) • (5, -7) • (4, -8) • None of the above A B C

8. Objective 3 • If the point (4, -5) is reflected across the x- axis, what will be its new coordinates? • (-4, 5) • (4, -5) • (4, 5) • (-4, -5) A

9. Objective 3 • A circle has a radius of 8 inches. The circle is dilated by reducing its radius by 40%. What is the radius of the reduced circle? • 4.0 cm • 4.8 cm • 4.1 cm • 4.4 cm

10. Objective 3 • Which best represents the top view of the 3-Dimensional figure shown below?

11. Objective 3 A B C D

12. Objective 3 • The right triangle shown below is drawn with a square adjacent to each side. Which equation represents the relationship between the lengths of the sides of the right triangle? • a2 + b2 = c2 • a2 + c2 = b2 • b2 + c2 = a2 • a2 + b2 > c2 c cm b cm a cm

13. Objective 3 • What will be the area of the shaded region? • (l x t ) – (t x t) –(1/2 x p x t) • (l x l ) – (t x t) –(1/2 x p x t) • (l x b) – (t x p) –(1/2 x p x t) • (l x b) – (t x t) –(1/2 x p x t) b cm p t l cm

14. Objective 3 • A company sells its advertising banners that are 30 ft long by 6 ft wide. For a certain requirement company needs to increase the length of banner by 40 inches. By how much the width of the banner increase in order to keep the same proportion between the length and the width of the banner? • 7 inches • 9 inches • 8 inches • 5 inches

15. Objective 3 • A hexagon with an area of 560 cm2 is dilated by a factor of 2. What is the area of the new hexagon? • 280 cm2 • 250cm2 • 40cm2 • 46 cm2

16. Objective 3 • A right triangle with leg lengths of 9 and 12 units are dilated by a scale of 2 to produce a new right triangle. What is the perimeter of the new triangle? • 22 units • 25 units • 14 units • None of the above

17. Objective 3 • The dimensions of the triangle are given below. Which is NOT a right triangle? • (1, 2, 3) • (5, 4, 9) • (1, 1, 3) • All of the above

18. Objective 3 • ΔDEF is shown on the coordinate grid. Which set of coordinates best represents a reflection of ΔDEF across the y-axis? • (3, 5), (2, 1), (7, 2) • (−3, −6), (−2, −2), (−7, −3) • (3, 6), (2, 2), (7, 3) • (3, −2), (2, 2), (7, 1)

19. Objective 3 • The top, right, and front views of a figure made of identical cubes are shown below. Which solid figure best represents these views?

20. Objective 3 • Mrs. Jones visited a botanical garden with dimensions of 550 feet by 600 feet. Mrs. Jones plans to create a similar botanical garden in her backyard with dimensions that are 1/50 of the dimensions of the garden she visited. Which dimensions could she use? • 275 ft by 300 ft • 11 ft by 12 ft • 110 ft by 120 ft • 11 ft by 600 ft

21. Objective 3 • Which figure can be placed along the segment labeled x millimeters to make the model below a correct representation of the Pythagorean Theorem?

22. Objective 3 • Which point on the coordinate grid satisfies the conditions x > 4 and y < −1? • Point A • Point B • Point C • Point D

23. Thank You!