Question

Calculate the distance between the points M=(2, -2) and L=(8, -9 in the coordinate plane

Answer 1

c =
`√(85)`

set up equation

to find the distance between these two points, we can use the pythagorean theorem
`a^2 + b^2 = c^2`

a is the horizontal distance or |x2 - x1|

b is the vertical distance or |y2 - y1|

c is the direct distance that we want to find

finding a and b

with the points (2, -2) and (8, -9)

x1 = 2

x2 = 8

y1 = -2

y2 = -9

plug in values to get

a = |x2 - x1| = |8 - 2| = |6| = 6

b = |y2 - y1| = |-9 - (-2)| = |-9 + 2| = |-7| = 7

finding c

now we can plug a and b into
`a^2 + b^2 = c^2` to find c

`6^2 + 7^2 = c^2`

36 + 49 =
`c^2`

85 =
`c^2`

c =
`√(85)`