Midpoint and Distance Quiz

Answer explanation

To calculate the distance between two points (x1, y1) and (x2, y2), we use the formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Substituting the values, we get sqrt((7 - 3)^2 + (1 - 4)^2) = sqrt(16 + 9) = sqrt(25) = 5. Therefore, the distance between the points is 5.

Tags

CCSS.HSG.GPE.B.7

Answer explanation

To find the midpoint, average the x-coordinates and y-coordinates separately. Midpoint = ((-2 + 4) / 2, (3 + (-1)) / 2) = (1, 0). Therefore, the midpoint is (1, 0).

Tags

CCSS.HSG.GPE.B.6

Answer explanation

Using the distance formula, the distance between the points (1, 2) and (4, 6) is calculated as sqrt((4-1)^2 + (6-2)^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. Therefore, the correct answer is sqrt(25).

Tags

CCSS.HSG.GPE.B.7

Answer explanation

To find the midpoint, average the x-coordinates and the y-coordinates separately. Midpoint = ((5+9)/2, (8+12)/2) = (7, 10). Therefore, the correct midpoint is (7, 10).

Tags

CCSS.HSG.GPE.B.6

Answer explanation

The distance between two points (x1, y1) and (x2, y2) is given by the formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Substituting the values, we get sqrt((3 - 0)^2 + (4 - 0)^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. Therefore, the distance between the points (0, 0) and (3, 4) is 5.

Tags

CCSS.HSG.GPE.B.7

Answer explanation

To calculate the distance between two points (-1, -1) and (2, 3), we use the distance formula: sqrt((2 - (-1))^2 + (3 - (-1))^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = sqrt(5^2) = sqrt(20)

Tags

CCSS.HSG.GPE.B.7

Answer explanation

To find the distance between two points (x1, y1) and (x2, y2), we use the formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Substituting the values, we get sqrt((4 - 1)^2 + (5 - 1)^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = sqrt(5^2) = sqrt(20). Therefore, the distance between the points (1, 1) and (4, 5) is sqrt(20).

Tags

CCSS.HSG.GPE.B.7

Answer explanation

The midpoint is calculated by averaging the x-coordinates and y-coordinates separately. So, (3+7)/2 = 5 and (7+3)/2 = 5. Therefore, the midpoint is (5, 5).

Tags

CCSS.HSG.GPE.B.6

Answer explanation

The midpoint formula averages the x-coordinates and y-coordinates separately. For (-3, -3) and (3, 3), the midpoint is ((-3+3)/2, (-3+3)/2) = (0, 0). Therefore, the correct answer is (0, 0).

Tags

CCSS.HSG.GPE.B.6

Answer explanation

The distance between the points (0, 0) and (6, 8) can be calculated using the distance formula, which gives a result of 10. Therefore, the correct answer is 10.

Tags

CCSS.HSG.GPE.B.7