Question

Two vertices of a right triangle have coordinates (5, 12) and (11, 12). The segment that connects these points is a leg of the triangle.

Which coordinate pair for the third vertex would create a right triangle?

Responses

​(19, 12)​
​, left parenthesis 19 comma 12 right parenthesis, ​

​(8, 20)​
​, left parenthesis 8 comma 20 right parenthesis, ​

​(8, 12)​
​, left parenthesis 8 comma 12 right parenthesis, ​

​(11, 4)​
​, left parenthesis 11 comma 4 right parenthesis, ​

Answer 1

The answer is (A) (11, 4).

Explanation: Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).

We can plot the given points on the co-ordinate plane as shown in the attached figure.

We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.

The lengths of the three sides are

`AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^(2) +BC^(2) } = \sqrt{6x^(2)+8^(2) } = √(100) = 10`

Thus, the correct option is (A).