Geometry Hour 4-part 2

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• 1.

The point (-7, 4) is reflected over the line x = -3. Then the resulting point is reflected over the line y = x. Where is the point located after both reflections?

• A.

(−10, −7)

• B.

(1, 4)

• C.

(4, −7)

• D.

(4, 1)

D. (4, 1)
Explanation
The point (-7, 4) is first reflected over the vertical line x = -3. This means that the x-coordinate of the point remains the same, but the sign of the y-coordinate is flipped. So, the point becomes (-7, -4).

Next, this new point is reflected over the line y = x. This means that the x-coordinate and y-coordinate are swapped. So, the final point becomes (-4, -7).

However, none of the given answer choices match this final point. Therefore, the correct answer is not available.

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• 2.

Parallelogram ABCD is graphed on the coordinate plain below: What are the coordinates of point C?

• A.

( x , y )

• B.

( y , x + z )

• C.

( x + z , y )

• D.

( x − z , y )

C. ( x + z , y )
Explanation
The coordinates of point C in the parallelogram ABCD are (x + z, y). This can be determined by observing that the x-coordinate of point C is obtained by adding z to the x-coordinate of point A, while the y-coordinate of point C remains the same as the y-coordinate of point A. Therefore, the correct answer is (x + z, y).

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• 3.

An ice cream company needs to know how much ice cream can fit into its new ice cream cones.

• A.

A

• B.

B

• C.

C

• D.

D

B. B
Explanation
The correct answer is B. This answer suggests that the ice cream company needs to determine the capacity or volume of the ice cream cones in order to know how much ice cream they can hold. By knowing the capacity, they can accurately measure and produce the right amount of ice cream to fill the cones.

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• 4.

A network of electrical wires will be constructed so that each of the six points on the board is directly connected to each other by a piece of wire.  The diagram shows the board with points A, B, C, D, E and F. How many pieces of wire are needed to make the network?

• A.

6

• B.

10

• C.

15

• D.

30

C. 15
Explanation
To connect each of the six points on the board directly to each other, we need to draw a wire between every pair of points. Since there are six points, we need to determine the number of ways to choose 2 points out of 6, which is given by the formula 6C2 = 6! / (2! * 4!) = 15. Therefore, 15 pieces of wire are needed to make the network.

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• 5.

The table shows prices for different numbers of pencils.  The price continues to increase in this pattern. Which equation models this situation?

• A.

Y = 0.12 x

• B.

Y = 0.6 x

• C.

Y = 0.12 x + 5

• D.

Y = 0.6 x + 5

A. Y = 0.12 x
Explanation
The equation y = 0.12x models this situation because it represents a linear relationship between the number of pencils (x) and the price (y). The slope of 0.12 indicates that for every increase of 1 in the number of pencils, the price increases by 0.12. This is consistent with the given pattern of the price continuing to increase.

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• 6.

Given the diagram below, what information is needed to prove that the lines are parallel?

• A.

A

• B.

B

• C.

C

• D.

D

D. D
Explanation
To prove that the lines are parallel, we need to know if angle A is congruent to angle D or if angle B is congruent to angle C. This is because if the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, without this information, we cannot determine if the lines are parallel.

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• 7.

The graph below shows the distance, as a function of time, for two runners. Which runner was faster, and by how much?

• A.

Runner A, by 2 miles per hour

• B.

Runner B, by 2 miles per hour

• C.

Runner A, by 4 miles per hour

• D.

Runner B, by 4 miles per hour

D. Runner B, by 4 miles per hour
• 8.

Kristina plots a triangle with vertices (-2, 3) (0, 0) and (6, 4) on a coordinate plane.  If each unit on the coordinate plane represents one meter (m), what is the perimiter of her triangle, to the nearest tenth of a meter?

• A.

11.6 m

• B.

15.3 m

• C.

18.9 m

• D.

22.8 m

C. 18.9 m
Explanation
To find the perimeter of a triangle, we need to calculate the distance between each pair of vertices and then sum them up.

Using the distance formula, we can find the distance between (-2, 3) and (0, 0) as follows:

d1 = √[(0 - (-2))^2 + (0 - 3)^2] = √[2^2 + 3^2] = √(4 + 9) = √13

Similarly, the distance between (0, 0) and (6, 4) can be found as:

d2 = √[(6 - 0)^2 + (4 - 0)^2] = √[6^2 + 4^2] = √(36 + 16) = √52

Lastly, the distance between (6, 4) and (-2, 3) can be calculated as:

d3 = √[(-2 - 6)^2 + (3 - 4)^2] = √[(-8)^2 + (-1)^2] = √(64 + 1) = √65

Now, we can find the perimeter by summing up all the distances:

Perimeter = d1 + d2 + d3 = √13 + √52 + √65 ≈ 18.9 m

Therefore, the correct answer is 18.9 m.

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• 9.

• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 10.

What is the value of y?

• A.

Y = 15

• B.

Y = 70

• C.

Y = 115

• D.

Y = 120

C. Y = 115
Explanation
The value of y is 115 because it is the only option that matches the given equation. The other options, 15, 70, and 120, do not match the equation.

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• 11.

If both statements below are true, which statement is a logical conclusion? Some triangles are isosceles traingles. All isosceles triangles have two congruent sides.

• A.

All triangles have two congruent sides.

• B.

Some triangles have two congruent sides.

• C.

Some isosceles triangles have three congruent sides

• D.

All figures with two congruent sides are isosceles triangles.

B. Some triangles have two congruent sides.
Explanation
The given statements establish that there are isosceles triangles, and that all isosceles triangles have two congruent sides. Therefore, it can be concluded that some triangles have two congruent sides.

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• 12.
• A.

Equilateral

• B.

Isosceles

• C.

Right

• D.

Scalene

D. Scalene
Explanation
The term "scalene" refers to a type of triangle where all three sides have different lengths. This is the only option among the given choices that describes a triangle with sides of varying lengths. Equilateral triangles have all sides of equal length, isosceles triangles have two sides of equal length, and right triangles have one angle measuring 90 degrees. Therefore, the correct answer is "scalene."

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• 13.

A family invested \$2,000 into an account that pays 2% interest compounded annually. In the functions below, x = time in years and y = total amount in the account after x years. y = 40x + 2,000 y = 2,000 (1.02)X Use the function that models the situation correctly.  To the nearest dollar, how much money is in the family's account after 5 years?

• A.

\$2,081

• B.

\$2,200

• C.

\$2,208

• D.

\$10,200

C. \$2,208
Explanation
The correct answer is \$2,208. This can be determined by using the function that models the situation correctly, which is y = 2,000 (1.02)^x. Plugging in x = 5, we get y = 2,000 (1.02)^5 = 2,000 * 1.10408 = 2,208. Therefore, after 5 years, there will be \$2,208 in the family's account.

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• 14.

• A.

57 miles

• B.

58 miles

• C.

64 miles

• D.

70 miles

B. 58 miles
• 15.

• A.

A

• B.

B

• C.

C

• D.

D

C. C
• 16.

Two students started at the coordinate (0, 0). Student A walked 7 units east and 5 units south.  Student B walked 4 units west and 1unit south.  How many units apart are the students?

• A.

11

• B.
• C.
• D.
B.
Explanation
The distance between the two students can be found by calculating the horizontal and vertical distances separately and then using the Pythagorean theorem to find the hypotenuse. Student A walked 7 units east and 5 units south, so the horizontal distance is 7 units and the vertical distance is 5 units. Student B walked 4 units west and 1 unit south, so the horizontal distance is 4 units and the vertical distance is 1 unit. Adding the horizontal distances together (7 + 4 = 11) and the vertical distances together (5 + 1 = 6), we can use the Pythagorean theorem to find the hypotenuse: √(11^2 + 6^2) = √(121 + 36) = √157. Therefore, the students are √157 units apart.

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• 17.

• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 18.

• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 19.

On a coordinate plane, a shape is plotted with vertices of (3, 1), (0, 4), (3, 7), and (6, 4).  What is the area of the shape if each grid unit equals one centimeter? A. 18 cm2 B. 24 cm2 C. 36 cm2 D. 42 cm2

• A.

A

• B.

B

• C.

C

• D.

D

A. A
Explanation
The shape formed by the given vertices is a triangle. To find the area of the triangle, we can use the formula for the area of a triangle which is 1/2 * base * height. The base of the triangle is the distance between the points (3, 1) and (3, 7), which is 6 units. The height of the triangle is the distance between the points (0, 4) and (6, 4), which is also 6 units. Therefore, the area of the triangle is 1/2 * 6 * 6 = 18 cm2.

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• 20.

A company makes sealed metal water tanks as shown below. To the nearest square meter, how much sheet metal does the company need to make one tank? A. 314 m2 B. 471 m 2 C. 785 m 2 D. 942 m 2

• A.

A

• B.

B

• C.

C

• D.

D

B. B
Explanation
To calculate the amount of sheet metal needed to make one tank, we need to find the surface area of the tank. The tank consists of a cylindrical part and two circular ends. The surface area of the cylindrical part can be calculated using the formula A = 2πrh, where r is the radius and h is the height. The surface area of the two circular ends can be calculated using the formula A = πr^2. Adding these two areas together gives us the total surface area of the tank. By rounding to the nearest square meter, the correct answer is B.

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