Question

On the coordinate plane, the vertices that define the hypotenuse of a triangle are located at (0,2) and (0,15). If the lengths of the two legs are whole number values, what could be the length of one leg?

a. 13
b. 10
c. 7
d. 17

Answer 1

The length of one leg of the right-angled triangle can be determined by finding the difference in the y-coordinates of the hypotenuse vertices, resulting in a whole number length of 13 units.

Step-by-step explanation:

The question relates to finding the length of a leg in a right-angled triangle where the coordinates of the hypotenuse are given, making it a question about the Pythagorean theorem.

The hypotenuse is vertical, which means one of the legs is a horizontal line and the other leg is the height between the two points (0,2) and (0,15). To find the length of the leg, we simply calculate the difference in the y-values of the two points, which means the length of one leg is 15 - 2 = 13 units.

Hence, the correct answer is a. 13, which is a whole number value as required by the question.