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# What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?

What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?

This problem would best be solved by graphing.  Since I don't know how to do graphing (is it even possible?) in the Wyzant Answers blank, I will explain what you will see...

After plotting the three points, you will see that the line from A to B is horizontal, since they have the same y coordinate.

You will also see that the line from B to C is vertical since they have the same x coordinate.

Since line segment AB is horizontal and line segment BC is vertical, they are perpendicular.

If two legs of a triangle are perpendicular, the triangle is a right triangle.

Let's find distance between the points, by using the formula d=√((x1 - x2)2+(y1 - y2)2

A(0 ,-6)    B(3 ,-6)      (x1 - x2)2 = (0 - 3)2 = (-3)2 = 9 ,   (y1 - y2)2 = (-6 - (-6))2 = 0
x1, y1             x2, y2
lABl = √(9+0) = 3 = a
B(3, -6)     C(3, -2)     (x1 - x2)2 = (3 - 3)2 = 0 ,   (y1 - y2)2 = (-6 - (-2))2 = (-6 + 2)2 = 16
x1, y1             x2, y2
lBCl = √16 = 4 = b
A(0 ,-6)     C(3, -2)     (x1 - x2)2 = (0 - 3)2 = 9 ,  (y1 - y2)2 = (-6 - (-2))2 = (-6 + 2)2 = 16
x1, y1              x2, y2
lACl = √(9+16) = 5 = c
c2 = a2 + b2   -----------> ΔABC is a right Δ

Well start off with a coordinate grid.  then add the dots and see if it is an acute triangle, obtuse triangle or right triangle.

A(0,-6) right 0 units and down 6 units

B(3,-6) right 3 units and down 6 units

C(3,-2) Right 3 units and down 2 units

connect the dots starting with A Going Right 3 units to B, From B to C you go Straight up 4 units to -2

The angle from A to B to C is a right angle. the triangle is a right triangle.

For extra credit use the Pythagorean Theorem to find the lengths of all three sides, You know from A to B is 3 units and from B to C is 4 units.

Pythagorean Theorem  is a^2 + B^2 = C^2   plug in 3 for A and 4 for B and solve the equation.

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