Mathletes Quiz 7 - Geometric Reasoning (L-Z)

What quadrant is the point (3.5, -1) located in?

• I

• II

• III

• IV

Answer explanation

The point (3.5, -1) has a positive x-coordinate and a negative y-coordinate. This places it in the fourth quadrant (IV), where x is positive and y is negative.

Tags

CCSS.6.NS.C.6B

What is the ordered pair for the reflection of point P (-2, -2.5) when it is reflected across the y-axis?

• (2, -2.5)

• (-2, 2.5)

• (2, 2.5)

• (-2, -2.5)

Answer explanation

To reflect point P (-2, -2.5) across the y-axis, change the sign of the x-coordinate. Thus, the reflection is (2, -2.5), which matches the correct answer choice.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Write the ordered pair that is located in Quadrant II.

• (-2, 5)

• (3, 4)

• (5, -6)

• (7, 8)

Answer explanation

In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. The ordered pair (-2, 5) fits this description, as -2 is negative and 5 is positive. The other options do not meet these criteria.

Tags

CCSS.6.NS.C.6B

What is the ordered pair for the reflection of Point A (-3, 4) when it is reflected over the x-axis?

• (-3, -4)

• (-3, 4)

• (3, -4)

• (3, 4)

Answer explanation

When reflecting a point over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. For Point A (-3, 4), the reflection is (-3, -4), making ( -3, -4) the correct answer.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Each unit on a coordinate plane is equivalent to 0.5 miles. Alex’s house is located at (-5, -4) and the library is located at (-5, 3). How far in miles is Alex’s house from the library?

• 3.5 miles

• 7 miles

• 35 miles

• 70 miles

Answer explanation

To find the distance between Alex's house at (-5, -4) and the library at (-5, 3), calculate the vertical distance: 3 - (-4) = 7 units. Since each unit is 0.5 miles, the distance is 7 * 0.5 = 3.5 miles.

Tags

CCSS.6.NS.C.8

Mia is riding her bike from her house to the park. If the park is located at (3, -5) and Mia lives 7 units away from the park, what is a possible coordinate of Mia’s house?

• A possible coordinate of Mia’s house is (3, 7).

• A possible coordinate of Mia’s house is (10, 0).

• A possible coordinate of Mia’s house is (0, -12).

• A possible coordinate of Mia’s house is (3, 2).

Answer explanation

Mia lives 7 units away from the park at (3, -5). The coordinate (3, 2) is 7 units directly above the park, making it a valid location for her house. The other options do not satisfy the distance requirement.

Tags

CCSS.HSG.GPE.B.7

Shahala and Paul are hiking by themselves in Hillsborough River State Park. Shahala is located at (2, -12) and Paul is located at (-5, -12). If each unit is equivalent to 2 miles, how many miles apart are Shahala and Paul?

• The distance between Shahala and Paul is 14 miles.

• The distance between Shahala and Paul is 7 miles.

• The distance between Shahala and Paul is 28 miles.

• The distance between Shahala and Paul is 10 miles.

Answer explanation

To find the distance between Shahala (2, -12) and Paul (-5, -12), calculate the difference in their x-coordinates: |2 - (-5)| = |2 + 5| = 7 units. Since each unit is 2 miles, the distance is 7 * 2 = 14 miles.

Tags

CCSS.6.G.A.3

Use the coordinate grid below to find the distance between points A and B.

• 5 units

• 7 units

• 15 units

• 20 units

Answer explanation

To find the distance between points A and B, use the distance formula: d = √((x2 - x1)² + (y2 - y1)²). After calculating, the distance is 7 units, making it the correct choice.

Tags

CCSS.6.NS.C.8

A square has an area of 49 units. One vertex of the square is located at (-2, 5). Which of the following could be the coordinates of another possible vertex?

• (-2, 2)

• (-2, -2)

• (-9, -5)

• (-2, -12)

Answer explanation

The area of the square is 49 units, so each side is 7 units long. From the vertex (-2, 5), moving down 7 units gives (-2, -2), which is a valid vertex. The other options do not maintain the square's properties.

Tags

CCSS.6.G.A.3

A square has a perimeter of 20 units. One vertex of the square is located at (-3, -3). Find the coordinates of another possible vertex.

• (2, -3)

• (8, 3)

• (2, 2)

• (0, 0)

Answer explanation

The perimeter of the square is 20 units, so each side is 5 units. Starting from (-3, -3), moving 5 units to the right gives (2, -3), which is a valid vertex. Other options do not maintain the square's properties.

Tags

CCSS.6.G.A.3