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

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3 Answers

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.