What is the distance between each pair of points?
Pair of points
(1,−3) and (1,7) = what distance?
(−9,4) and (−2,4)= what distance?
The distance between (1,-3) and (1,7) is 10 units (vertical distance).
The distance between (-9,4) and (-2,4) is 7 units (horizontal distance).
To find the distance between each pair of points, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the pair of points (1, -3) and (1, 7):
x1 = 1, y1 = -3
x2 = 1, y2 = 7
Distance = √((1 - 1)^2 + (7 - (-3))^2)
= √((0)^2 + (10)^2)
= √(0 + 100)
= √100
= 10
So, the distance between the points (1, -3) and (1, 7) is 10 units.
For the pair of points (-9, 4) and (-2, 4):
x1 = -9, y1 = 4
x2 = -2, y2 = 4
Distance = √((-2 - (-9))^2 + (4 - 4)^2)
= √((7)^2 + (0)^2)
= √(49 + 0)
= √49
= 7
So, the distance between the points (-9, 4) and (-2, 4) is 7 units.
To find the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the given pairs of points using the distance formula:
1. For (1, -3) and (1, 7):
x1 = 1, y1 = -3
x2 = 1, y2 = 7
Substituting these values into the distance formula, we have:
d = sqrt((1 - 1)^2 + (7 - (-3))^2)
= sqrt(0^2 + 10^2)
= sqrt(0 + 100)
= sqrt(100)
= 10
Therefore, the distance between the points (1, -3) and (1, 7) is 10 units.
2. For (-9, 4) and (-2, 4):
x1 = -9, y1 = 4
x2 = -2, y2 = 4
Substituting these values into the distance formula, we have:
d = sqrt((-2 - (-9))^2 + (4 - 4)^2)
= sqrt((-2 + 9)^2 + 0^2)
= sqrt(7^2 + 0^2)
= sqrt(49 + 0)
= sqrt(49)
= 7
Therefore, the distance between the points (-9, 4) and (-2, 4) is 7 units.