Math 6 - Exploring the Coordinate Plane

Where would the point (-2, 2) and (4, -2) be placed on the coordinate grid?

Tags

CCSS.6.NS.C.6B

Plot the point (3, 4) on the coordinate plane. Which quadrant is it located in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

The point (3, 4) has a positive x-coordinate and a positive y-coordinate, placing it in Quadrant I, where both coordinates are positive.

Tags

CCSS.6.NS.C.6B

What are the coordinates of the point located 5 units to the right and 2 units up from the origin?

• (5, 2)

• (2, 5)

• (-5, 2)

• (5, -2)

Answer explanation

Starting from the origin (0, 0), moving 5 units to the right increases the x-coordinate to 5, and moving 2 units up increases the y-coordinate to 2. Thus, the coordinates are (5, 2).

Tags

CCSS.5.G.A.2

If point A is at (2, 3) and point B is at (2, 7), what is the distance between them?

• 3 units

• 4 units

• 5 units

• 6 units

Answer explanation

To find the distance between points A(2, 3) and B(2, 7), use the distance formula for vertical points: |y2 - y1|. Here, |7 - 3| = 4 units. Thus, the distance is 4 units.

Tags

CCSS.HSG.GPE.B.7

Translate the point (4, -3) 2 units left and 5 units up. What are the new coordinates?

• (2, 2)

• (6, 2)

• (2, -8)

• (6, -8)

Answer explanation

To translate the point (4, -3) 2 units left, subtract 2 from the x-coordinate: 4 - 2 = 2. To move 5 units up, add 5 to the y-coordinate: -3 + 5 = 2. The new coordinates are (2, 2), which is the correct answer.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Reflect the point (-5, 6) across the x-axis. What are the new coordinates?

• (-5, -6)

• (5, 6)

• (5, -6)

• (-5, 6)

Answer explanation

To reflect the point (-5, 6) across the x-axis, we change the sign of the y-coordinate. Thus, the new coordinates are (-5, -6), making the correct answer (-5, -6).

Tags

CCSS.6.NS.C.6B

Which quadrant is the point (-3, -4) located in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

The point (-3, -4) has both coordinates negative, which places it in Quadrant III. In this quadrant, x-values are negative and y-values are also negative.

Tags

CCSS.6.NS.C.6B

What are the coordinates of the point that is 3 units left and 4 units down from (0, 0)?

• (3, 4)

• (-3, -4)

• (-3, 4)

• (3, -4)

Answer explanation

Starting from (0, 0), moving 3 units left means subtracting 3 from the x-coordinate, resulting in -3. Moving 4 units down means subtracting 4 from the y-coordinate, resulting in -4. Thus, the coordinates are (-3, -4).

Tags

CCSS.6.NS.C.6B

If point C is at (1, 1) and point D is at (1, 5), what is the distance between them?

• 2 units

• 3 units

• 4 units

• 5 units

Answer explanation

To find the distance between points C(1, 1) and D(1, 5), use the distance formula for vertical points: |y2 - y1|. Here, |5 - 1| = 4 units. Thus, the distance is 4 units.

Tags

CCSS.6.G.A.3

Translate the point (-2, 3) 4 units right and 1 unit down. What are the new coordinates?

• (2, 2)

• (2, 4)

• (-6, 2)

• (6, 4)

Answer explanation

To translate the point (-2, 3) 4 units right, add 4 to the x-coordinate: -2 + 4 = 2. To move 1 unit down, subtract 1 from the y-coordinate: 3 - 1 = 2. The new coordinates are (2, 2), which is the correct answer.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5