1. What is the equation of a line that is parallel to −3x+4y=4 and passes through the point (4, 0) ?

2. In △ABC, the coordinates of vertices A and B are A(1,−1) and B(3,2).

For each of the given coordinates of vertex C, is △ABC a right triangle?

Select Right Triangle or Not a Right Triangle for each set of coordinates.

3.

4.

Guest Nov 2, 2018

#1**+1 **

1)

\(-3x+4y=4 \\ y = \dfrac 3 4 x + 1 \\ slope = \dfrac 3 4 \\ \text{now we construct a line with slope }\dfrac 3 4 \text{ passing through }(4,0)\\ \text{using point slope form}\\ (y-0) = \dfrac 3 4 (x-4) \\ y = \dfrac 3 4 x - 3 \\ -3x + 4y = -12\)

Rom
Nov 4, 2018

#2**+1 **

2)

I guess the easiest way to do this is check the Pythagorean theorem for a right triangle.

For each value of c find the length squared of each of the 3 sides of the triangle and sort them.

Then if the triangle is a right triangle the sum of the two smaller squared sides will equal

the largest squared side.

I'm going to let you slog through the arithmetic. I suggest using a spreadsheet or something.

Rom
Nov 4, 2018