Find the distance between the two points in simplest radical form.
(8,−1) and (2,−9)
To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (8, -1) and (2, -9):
x1 = 8
y1 = -1
x2 = 2
y2 = -9
Plugging these values into the distance formula:
d = sqrt((2 - 8)^2 + (-9 - (-1))^2)
= sqrt((-6)^2 + (-9 + 1)^2)
= sqrt(36 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100)
= 10
Therefore, the distance between the two points in simplest radical form is 10.
To find the distance between two points (x1, y1) and (x2, y2), you can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, the coordinates are (8, -1) and (2, -9). Let's substitute the values into the formula:
d = √[(2 - 8)^2 + (-9 - (-1))^2]
Simplifying inside the square root:
d = √[(-6)^2 + (-9 + 1)^2]
d = √[36 + (-8)^2]
d = √[36 + 64]
d = √100
d = 10
Therefore, the distance between the two points is 10 units.
To find the distance between two points, we can use the distance formula. The formula is derived from the Pythagorean theorem.
The distance formula is given by:
√((x2 - x1)^2 + (y2 - y1)^2)
In this case, point 1 has coordinates (x1, y1) = (8, -1) and point 2 has coordinates (x2, y2) = (2, -9).
Substituting these values into the distance formula, we get:
√((2 - 8)^2 + (-9 - (-1))^2)
Simplifying:
√((-6)^2 + (-9 + 1)^2)
√(36 + (-8)^2)
Calculating:
√(36 + 64)
√(100)
= 10
Therefore, the distance between the two points (8,-1) and (2,-9) is 10 units.