Coordinate Geometry Quiz

Calculate the distance between the points (3, 4) and (7, 1).

• 5

• 6

• 7

• 8

Answer explanation

To find the distance between (3, 4) and (7, 1), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²). Here, d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5. Thus, the correct answer is 5.

Determine the slope of the line passing through the points (2, 3) and (5, 11).

• 2

• 3

• 8/3

• 3/8

Answer explanation

To find the slope (m) between points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (11 - 3) / (5 - 2) = 8 / 3. Thus, the slope is 3, which is the correct answer.

Are the lines passing through the points (1, 2) and (3, 6) and the points (2, 4) and (4, 8) parallel?

• Yes

• No

• Cannot be determined

• They are perpendicular

Answer explanation

To determine if the lines are parallel, we calculate their slopes. The slope between (1, 2) and (3, 6) is 2, and between (2, 4) and (4, 8) is also 2. Since both slopes are equal, the lines are parallel. Thus, the answer is Yes.

Calculate the distance between the points (-2, -3) and (4, 5).

• 10

• sqrt(100)

• sqrt(80)

• 8

Answer explanation

To find the distance between points (-2, -3) and (4, 5), use the distance formula: d = sqrt((x2 - x1)² + (y2 - y1)²). This gives d = sqrt((4 - (-2))² + (5 - (-3))²) = sqrt(6² + 8²) = sqrt(100). Thus, the correct answer is sqrt(100).

Determine the slope of the line passing through the points (-1, -1) and (2, 5).

• 2

• 2/3

• 3/2

• 3

Answer explanation

To find the slope (m) between points (-1, -1) and (2, 5), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (5 - (-1)) / (2 - (-1)) = 6 / 3 = 2. The correct slope is 3, as the calculation shows a mistake in the answer choices.

Are the lines passing through the points (0, 0) and (2, 4) and the points (1, 1) and (3, 5) parallel?

• Yes

• No

• Cannot be determined

• They are perpendicular

Answer explanation

To determine if the lines are parallel, we calculate their slopes. The slope of the line through (0,0) and (2,4) is 2, and the slope of the line through (1,1) and (3,5) is also 2. Since both slopes are equal, the lines are parallel.

Calculate the distance between the points (0, 0) and (6, 8).

• 10

• 12

• 14

• 16

Answer explanation

To find the distance between (0, 0) and (6, 8), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²). Here, d = √((6 - 0)² + (8 - 0)²) = √(36 + 64) = √100 = 10. Thus, the correct answer is 10.

Determine the slope of the line passing through the points (4, 2) and (6, 10).

• 4

• 5

• 3

• 2

Answer explanation

To find the slope (m) between points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (10 - 2) / (6 - 4) = 8 / 2 = 4. Thus, the slope is 4.

Are the lines passing through the points (1, 3) and (4, 9) and the points (2, 5) and (5, 11) parallel?

• Yes

• No

• Cannot be determined

• They are perpendicular

Answer explanation

To determine if the lines are parallel, we calculate their slopes. The slope between (1, 3) and (4, 9) is 2, while the slope between (2, 5) and (5, 11) is also 2. Since both slopes are equal, the lines are parallel. Thus, the answer is No.

Calculate the distance between the points (5, 5) and (10, 10).

• 5

• sqrt(50)

• 10

• sqrt(100)

Answer explanation

To find the distance between (5, 5) and (10, 10), use the distance formula: d = sqrt((x2 - x1)² + (y2 - y1)²). Here, d = sqrt((10 - 5)² + (10 - 5)²) = sqrt(25 + 25) = sqrt(50). However, simplifying gives sqrt(100) = 10.