Question

If ABC is a right triangle with B the right angle, A=(-3,2) and B =(2,5), find possible

coordinates for C

Answer 1

The coordinates for point C in the right triangle ABC can be found using the distance formula and the Pythagorean theorem.

Step-by-step explanation:

The coordinates for point C in the right triangle ABC can be found by using the distance formula and the Pythagorean theorem.

Using the distance formula, we can find the distance between points A and B:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((2 - (-3))^2 + (5 - 2)^2) = sqrt(25 + 9) = sqrt(34)

Next, we can use the Pythagorean theorem to find the length of the hypotenuse AB:

c = sqrt(a^2 + b^2)

c = sqrt((-3 - 2)^2 + (2 - 5)^2) = sqrt(25 + 9) = sqrt(34)

Since c is the length of the hypotenuse, the point C can be at any location on a circle with radius sqrt(34) centered at B.