Answer:

1. Using the distance formula:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

d = sqrt((-2-1)^2 + (-1-4)^2)

d = sqrt((-3)^2 + (-5)^2)

d = sqrt(9 + 25)

d = sqrt(34)

Therefore, H is sqrt(34) units away from M.

2. Using the distance formula:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

d = sqrt((-2-1)^2 + (-1-4)^2)

d = sqrt((-3)^2 + (-5)^2)

d = sqrt(9 + 25)

d = sqrt(34)

Therefore, the distance between F and M is sqrt(34) units.

3. Using the distance formula:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

d = sqrt((-4-7)^2 + (3-6)^2)

d = sqrt((-11)^2 + (-3)^2)

d = sqrt(121 + 9)

d = sqrt(130)

Therefore, (7, 6) is sqrt(130) units away from (-4, 3).

4. Using the distance formula:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

d = sqrt((-6-15)^2 + (15-(-5))^2)

d = sqrt((-21)^2 + (20)^2)

d = sqrt(441 + 400)

d = sqrt(841)

d = 29

Therefore, the distance between (15, -5) and (-6, 15) is 29 units.

5. Using the distance formula:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

d = sqrt((0-8)^2 + (5-0)^2)

d = sqrt((-8)^2 + (5)^2)

d = sqrt(64 + 25)

d = sqrt(89)

Therefore, the distance between (8, 0) and (0, 5) is sqrt(89) units.

1. To find the distance between twopoints, the formula is D = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) is the position of the first point and (x2, y2) is the position of the second point. In this case, H(1, 4) and M(-2, -1) are the positions of the two points, so the distance is given by D = √((1 - -2)² + (4 - (-1))²) = √(5) = 2.236.

2. The formula for finding the distance between two points is given by D = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the positions of the points. In this case, F(1, 4) is the position of the first point and M(-2, -1) is the position of the second point, so we have D = √((1 - (-2))² + (4 - (-1))²) = √(11) = 3.316.

3. The distance between two points can be found by the following formula: D = √((x2 - x1)² + (y2 - y1)²). (7, 6) is the first point and (-4, 3) is the second point, so. the distance is given by D = √((7 - (-4))² + (6 - 3)²) = √(9 + 9) = √18 = 4.243.

4. To find the distance between points (15, -5) and (-6, 15), we use the formula: D = √((x2 - x1)² + (y2 - y1)²). We have (15, -5) and (-6, 15), so the distance is given by: D = √((15 + 6)² + (-5-15)²) = √(84) = 9.256.

5. The distance between the two points is given by the formula D = √((x2 - x1)² + (y2 - y1)²). So we have the points (8, 0) and (0, 5) and the distance is given by:

D = √((0 - 8)² + (5 - 0)²) = √(64) = 8.

So the distance between the points (8, 0) and (0, 5) is 8, the square root of 64.