Question

Find the slope between each pair of points. Then, using the Pythagorean Theorem, find the distance between each pair of points. Distance should be provided in exact form, no decimals. ( − 10 , − 3 ) and ( − 6 , 6 )

Answer 1

Slope = 2.25 units

Distance = 10 units

Explanation:

We are given the coordinates

(10,-3),(-6,6)

Slope is give by:

`(x_1,y_1),(x_2,y_2)\\\\\text{Slope} = (y_2-y_1)/(x_2-x_1)\\\\`

Putting values, we get

`\text{Slope} = (6-(-3))/(-6-(-10))\\\\=(9)/(4) = 2.25`

Distance between two points based on Pythagoras theorem is given by:

`(x_1,y_1),(x_2,y_2)\\\\d = √((y_2-y_1)^2 +(x_2-x_1)^2)`

Putting values, we get,

`d = √((6-(-3))^2 + (-6+10)^2)\\d = √(81+16)\\d = 9.84\\d \approx 10\text{ units}`