About Vertices of a Right Triangle:

In some cases, we will be asked to determine if three points are the vertices of a right triangle. We can accomplish this by finding the distance between each pair of points given. Once we know each distance, we can match this up with our Pythagorean formula. If the three points are the vertices of a right triangle, then it will be true that the square of the largest distance or hypotenuse is equal to the sum of each other distance squared.

Test Objectives
  • Demonstrate an understanding of the Pythagorean Formula
  • Demonstrate an understanding of the distance formula
  • Demonstrate the ability to determine if three points are the vertices of a right triangle
Vertices of a Right Triangle Practice Test:

#1:

Instructions: determine if the given points are the vertices of a right triangle.

$$a)\hspace{.2em}(-5,3), (6,0), (5,5)$$

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#2:

Instructions: determine if the given points are the vertices of a right triangle.

$$a)\hspace{.2em}(4,-3), (4,1), (2,1)$$

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#3:

Instructions: determine if the given points are the vertices of a right triangle.

$$a)\hspace{.2em}(-9,4), (2,6), (1,-5)$$

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#4:

Instructions: determine if the given points are the vertices of a right triangle.

$$a)\hspace{.2em}(6,4), (-5,1), (-7,-2)$$

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#5:

Instructions: determine if the given points are the vertices of a right triangle.

$$a)\hspace{.2em}(-2,5), (1,3), (-1,0)$$

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Written Solutions:

#1:

Solutions:

a) Yes, these are the endpoints of a right triangle. sketching a right triangle with endpoints (-5, 3), (6,0), and (5,5)

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#2:

Solutions:

a) Yes, these are the endpoints of a right triangle. sketching a right triangle with endpoints (4, -3), (4,1), and (2,1)

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#3:

Solutions:

a) No, these are not the endpoints of a right triangle. sketching a right triangle with endpoints (-9, 4), (2,6), and (1,-5)

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#4:

Solutions:

a) No, these are not the endpoints of a right triangle. sketching a right triangle with endpoints (6, 4), (-5,1), and (-7,-2)

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#5:

Solutions:

a) Yes, these are the endpoints of a right triangle. sketching a right triangle with endpoints (-2, 5), (1,3), and (-1,0)

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