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?

​ (11, 4) ​

​ (8, 20) ​

​ (19, 12) ​

​ (8, 12) ​

Answer 1

point (11,4) is directly below point (11,20) so a segment drawn between these two points would make a right angle.

Answer 2

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

Step-by-step 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=√(AB^2+BC^2)=√(6^2+8^2)=√(100)=10.`

Thus, the correct option is (A).