Hi phoenix9801

In the given solution, they are not calculating the slope.
They are calculating the length of the base and height of the right angled triangle.

Hence the sign won't matter.

base = |x2-x1|= |3-(-5)| =8
height = |y2-y1| = |1-7| = 6

For the 2nd question, it doesn't matter which side of the triangle you take as base. But it's advisable to chose |x2-x1| as the base for better understanding.

phoenix9801 wrote: Question 2: How to you allays know which side is a, b, or c? is the Y-coordinate is always the height and x-coordinate is always the base?

Here points a,b & c are just the notations, you can use them to represent any of the sides of the triangle.
Here the co-ordinate plane represents a 2-dimensional plane system, where the coordinates of a point are a pair of numbers that define its exact location on a 2-dimensional plane.
The co-ordinates of a point are written as an ordered pair. for example a(4,5), b(6,2) etc
Let a(x,y)
"x" specifies how far along the x (horizontal) axis the point is.
"y" specifies how far up or down the y (vertical) axis to go.
all are in respect to the origin where O(x,y) = O(0,0).

Slop = y^2 - y^1 / x^2 - x^1 =

Here the notation is wrong
Slop = y2 - y1/ x2 - x1

The question is asking you to find the distance between the two points not the slope of the line, they(the distance b/w two points and the slope of the line) are not same.

The distance can be calculated using the pythagoras' theorem.