Question

Two vertices of a right triangle have coordinates ( 9 , 1 ) and (;6 , - 1 ) Select each ordered pair that could be the coordinates of the third vertex ( 9 , - 1 ) ( 6 , 1 ) ( 1 , - 1 ) ( 6 , 9 ) ​

Answer 1

Option A: $(9,-1)$ is the third vertex

Option B: $(6,1)$ is the third vertex.

Explanation:

The two vertices of the right triangle are $(9,1)$ and $(6,-1)$

The third vertex of the right triangle can be determined by plotting the points in the graph.

Option A: $(9,-1)$

By plotting the points $(9,1)$, $(6,-1)$ and the third vertex $(9,-1)$ in the graph, the the hypotenuse of the triangle passes through the vertices $(9,1)$ and $(6,-1)$

The legs of the triangle passes through the vertices $(9,1)$, $(9,-1)$ and $(6,-1)$, $(9,-1)$

Hence, the third vertex $(9,-1)$ forms a right triangle.

Therefore, Option A is the correct answer.

Option B: $(6,1)$

By plotting the points $(9,1)$, $(6,-1)$ and the third vertex $(6,1)$ in the graph, the hypotenuse of the triangle passes through the vertices $(9,1)$ and $(6,-1)$

The legs of the triangle passes through the vertices $(9,1)$, $(6,1)$ and $(6,1)$ , $(6,-1)$

Hence, the third vertex $(6,1)$ forms a right triangle.

Therefore, Option B is the correct answer.

Option C: $(1,-1)$

By plotting the points $(9,1)$, $(6,-1)$ and the third vertex $(1,-1)$ in the graph, we can see that the three vertices does not make a right angled triangle.

Hence, the third vertex $(1,-1)$ does not form a right triangle.

Therefore, Option C is not the correct answer.

Option D: $(6,9)$

By plotting the points $(9,1)$, $(6,-1)$ and the third vertex $(6,9)$ in the graph, we can see that the three vertices does not make a right angled triangle.

Hence, the third vertex $(6,9)$ does not form a right triangle.

Therefore, Option D is not the correct answer.