Question

Determine if triangle XYZ with coordinates X (1, 1), Y (5, 6), and Z (6, 2) is a right triangle. Use evidence to support your claim. If it is not a right triangle, what changes can be made to make it a right triangle? Be specific.




Question 2
Triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes. You must show all of your work to receive credit.

Triangles ABC and DEF are shown. A is at 4, 2. B is at 4, 5. C is at 1, 2. D is at 2, negative 4. E is at 5, negative 4. F is at 2, negative 1.

Answer 1

@paki can you please help me:(

Answer 2

@SolomonZelman please help me

Answer 3

\(\normalsize\color{black}{ \rm{XY}}\)\(\normalsize\color{black}{ =\sqrt{(1-6)^2+(1-5)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{41}}\)

\(\normalsize\color{black}{ \rm{XZ}}\)\(\normalsize\color{black}{ =\sqrt{(1-2)^2+(1-6)^2}=\sqrt{(-1)^2+(-5)^2}=\sqrt{26}}\)

\(\normalsize\color{black}{ \rm{YZ}}\)\(\normalsize\color{black}{ =\sqrt{(5-6)^2+(6-2)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{17}}\)

Answer 4

\(\normalsize\color{black}{ \sqrt{17}^2 + \sqrt{26}^2= \sqrt{41}^2}\)

\(\normalsize\color{black}{ 17 + 26= 41}\)

\(\normalsize\color{black}{ 43= 41}\)

Answer 5

No it is not a right triangle

Answer 6

@jigglypuff314 HOW WOULD I MAKE IT INTO A TRIANGLE?

Answer 7

it is a triangle, because (as you can see, when I tried to prove that it is not a right triangle using a²+b²=c²) that it is a triangle, because the sum of 2 smaller sides is greater than the biggest side.
Also if you have 3 points and just connect them together, wouldn't that be a triangle ?