Answer:
perpendicular:
parallel:
Step-by-step explanation:
original line:
y = -5x + 5
=> 5x + y = 5
m = -5/1 = -5
perpendicular:
m = 1/5
L: x - 5y = k
(7, -5) -> L
7 - 5 * (-5) = k
=> 7 + 25 = 32 = k
L: x - 5y = 32
parallel:
m = -5
L: 5x + y = k
(7, -5) -> L
35 - 5 = 30 = k
L: 5x + y = 30
Hey there! I'm happy to help!
Imagine the line that is created when you connect the two points (the distance between the two points).
You can create a right triangle where this distance is the hypotenuse where the two legs are the change in x and y. So, if you take those changes in x and y, you can use the Pythagorean Theorem (a²+b²=c²) to find the distance between the two points, which is the hypotenuse.
Our change in x is 9 because 9-0 is 9.
We square it
9²=81
Our change in y is 5 as -1-(-6) or -1+6 is 5.
5²=25
We add these.
81+25=106
We square root and round to the nearest tenth.
√106≈10.3
So, our distance is 10.3.
This Pythagorean Theorem method actually gives us a formula called the distance formula that you can use to find the distance between points.
Have a wonderful day and keep on learning! :D