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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.

Nov 2, 2018

#1
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1)

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

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Nov 4, 2018
#2
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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.

Nov 4, 2018