8th grade geometry

Question 1

A rectangular park is 59 m long and 49 m wide. Instead of walking along two sides, you cut across the diagonal. How many metres shorter is the shortcut? Round to the nearest metre.

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Question 2

Find the distance between (−4, −4) and (4, −10).

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Question 3

Two parallel lines are cut by a transversal. One angle is 35°. What is its co-interior (same-side interior) partner?

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Question 4

What is each interior angle of a regular polygon with 12 sides, in degrees?

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Question 5

A label wraps exactly once around a can with radius 2 cm and height 12 cm (no overlap, no top or bottom). Its area is kπ cm². What is k?

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Question 6

A 5 by 2 rectangle is dilated by scale factor 3. What is the area of the image?

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Question 7

A right triangle has hypotenuse 10 ft and one leg 6 ft. How long is the other leg, in ft?

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Question 8

A cylinder has radius 2 m and height 15 m. Its volume is kπ m³. What is k?

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Question 9

A is (6, 5) and its image A′ is (5, 0). The translation moves every point by (a, b). What are a and b? Type them like (2, −3).

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Question 10

A cylinder has volume 96π m³ and height 6 m. What is its radius, in m?

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Question 11

A box is 4 cm by 6 cm by 12 cm. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner, in cm?

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Question 12

A right triangle has hypotenuse 5 m and one leg 4 m. How long is the other leg, in m?

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Question 13

Reflect (2, −1) in the x-axis. Type the image like (2, −3).

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Question 14

After a reflection, is the image congruent to the original (same size and shape)?

• A. Yes, congruent
• B. No, only similar

Question 15

In a triangle the two opposite interior angles are (x + 15)° and (2x + 1)°. The exterior angle is 97°. Find x.

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Question 16

Triangle PQR has P(0, 0), Q(2, 0), R(0, 3). It is translated by (4, 3). Where does Q go?

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