NEED HELP ASAP!

Question

Are the points A(3,5), B(0,2) and C(-2,10) the vertices of a right triangle? Justify your answer

The endpoints of the diameter of a circle are (-5,1) and (3,-5). Find the center and the radius of the circle. (write the equation of the circle in standard form)

Answer 1

First question has two ways of solving. 1) use the slope formula to show that two sides are perpendicular to each other (slopes are negative reciprocals of each other), and 2) use the distance formula and the Pythagorean theorem to show that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The second question involves the use of the midpoint formula to find the center, and the distance formula to find the radius (with is half the diameter).

Slope formula: m = (y₂ - y₁)/(x₂ - x₁)

Distance formula: d = sqrt((y₂ - y₁)²+(x₂ - x₁)²)

Midpoint formula: M = ((x₂ + x₁)/2, (y₂ + y₁)/2)