Graphing, slope, right triangle....

Question

Use the following ordered pairs: (-5,5), (-5,-8), (8,5)
1. Calculate each side of the triangle that is formed by these points
2. Calculate the slope of each side of the triangle
3. Do the points form a right triangle? Verify your findings using two methods (one related to side length and one related to the slope of the lines)
4. Is the triangle formed symmetric in any way? If so, how? (Over an axis/origin)?
5. Is this triangle isosceles?

Answer 1

Use the following ordered pairs: (-5,5), (-5,-8), (8,5)  sketch the triangle to "see" more

 

1. Calculate each side of the triangle that is formed by these points

use the distance formula  same as  pythagorean theorem

(the square of the hypotenuse  = sum of the squares of the legs of the right triangle.The hypotenuse is the longest side and opposite the right angle )

c^2 = a^2 + b^2  a = x2-x1 and b = y2 -y1  for 2 points (x1,y1) and (x2, y2) 

remember only use positive value for distance

example using (-5, -8) and (8,5) the distance    = positive square root of { (-5-8)^2 + (5 - - 8)^2 }

√(-13)² + 13²  = √338 = 18.38 rounded to 18 

  

2. Calculate the slope of each side of the triangle

slope is the  ratio of change in y /  corresponding  change in x  = (y2- y1)/(x2 - x1) for any 2 points on the line (x1,y1) and (x2, y2)

 

3. Do the points form a right triangle? yes  Verify your findings using two methods (one related to side length and one related to the slope of the lines)

if the product of the slope = -1 then the lines are perpendicular.  forms a right angle. Also Need to verify with side lengths

 

4. Is the triangle formed symmetric in any way? If so, how? (Over an axis/origin)?yes 2 side lengths are equal from point at (-5,5) 

 

5. Is this triangle isosceles? yes 2 sides of equal lengths  (13 units)