Question

Need help with pre-cal

Answer 1

A plot of the points A(-2, 11), B(5, 7), C(1, 0) is given by the option;

• D

• The triangle is a right triangle given that (AC)² = (AB)² + (BC)²

• The area of the ∆ABC is 32.5 square units.

• Sum of the squares of the lengths of the legs of the triangle = 130

• Square of the length of the hypotenuse of the triangle = 130

How can ∆ABC be proven to be a right triangle from its dimensions?

The coordinates of the vertices of the triangle are;

A = (-2, 11), B = (5, 7), C = (1, 0)

Therefore, on the coordinate plane, we have;

The highest and leftmost point of the triangle is the vertex, A

The second highest and rightmost point of the triangle is the vertex, B

The vertex of the triangle that is midway between A and B and the lowest vertex of the triangle is the vertex C

• The correct option that shows the points ABC and triangle ABC is the option D.

The lengths of the sides of the triangle are;

AB = √((-2 - 5)² + (11 - 7)²) = √(65)

BC = √((5 - 1)² + (7 - 0)²) = √(65)

AC = √((-2 - 1)² + (11 - 0)²) = √(130)

Therefore;

(AC)² = 130 = (AB)² + (BC)² = 65 + 65

Which gives;

• (AC)² = (AB)² + (BC)²

Therefore;

• ∆ABC is a right triangle, from the definition of a right triangle.

The legs of ∆ABC are AB and BC

AC is the hypotenuse of ∆ABC

The area of ∆ABC is therefore;

Area = (1/2) × AB × BC

Which gives;

Area of ∆ABC = (1/2) × √(65) × √(65)

√(65) × √(65) = 65

• Area of ∆ABC = (1/2) × 65 = 32.5

(AB)² + (BC)² = 65 + 65 = 130

Therefore;

• Sum of the squares of the lengths of the legs of the triangle = 130

(AC)² = 130

• Square of the length of the hypotenuse of the triangle = 130

Learn more about right triangles here:

brainly.com/question/2284306

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