find the length of the line segment joining the points whose coordinates are (-3,1) and (5, -5)
A.10
B.2 times square root of 10
C. 100
D. square root of 10
change in x from -3 to +5 = 8
change in y from 1 to -5 = -6
hypotenuse = sqrt (64 + 36) = sqrt 100 = 10
To find the length of a line segment joining two points in a coordinate plane, you can use the distance formula.
The distance formula for finding the distance between two points (x₁, y₁) and (x₂, y₂) is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's plug in the coordinates of the two points (-3,1) and (5, -5) into the formula:
x₁ = -3, y₁ = 1
x₂ = 5, y₂ = -5
d = √((5 - (-3))² + (-5 - 1)²)
= √(8² + (-6)²)
= √(64 + 36)
= √100
= 10
Therefore, the length of the line segment joining the points (-3,1) and (5, -5) is 10 units.