SOLUTION
First , we need to get the distance between each point , we can get their distance using the distance formula.
Point D to Point E
- D = √(x2-x1)²+(y2-y1)²
- D = √(5-2)²+(4-(-2))²
- D = √(5-2)²+(4+2)²
- D = √(3)²+(6)²
- D = √9-36
- D = √45 units
Point E to Point F
- D = √(x2-x1)²+(y2-y1)²
- D = √(-4-5)²+(1-4)²
- D = √(-9)²+(-3)²
- D = √81+9
- D = √90 units
Point F to Point D
- D = √(x2-x1)²+(y2-y1)²
- D = √(-4-2)²+(1-(-2))²
- D = √(-4-2)²+(1+2)²
- D = √(-6)²+(3)²
- D = √36+9
- D = √45 units
Proving that they forms a right triangle,
We then Use the pythagorean theorem
We got that a = √45 , b = √45 , and c = √90
Substituting the value of a , b , and c to the formula of pythagorean.
- (√45)²+(√45)² = (√90)²
- 45 + 45 = 90
- 90 = 90
Hence , Proved that the vertices form a right triangle.
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