Distance and Midpoint Formulas

These flashcards cover the concepts of distance, midpoint, and area calculation for geometric figures.

What is the formula to calculate the distance between two points P1(x1, y1) and P2(x2, y2)?

Distance = √[(x2-x1)² + (y2-y1)²]

How do you calculate the distance between the points A(5,8) and B(-1,0)?

Plug in the values: √[(-1-5)² + (0-8)²] = √[36 + 64] = √100 = 10.

What is the Midpoint Formula?

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

What is the midpoint of the endpoints (-2, 3) and (4, -2)?

Midpoint = [(2+4)/2, (3+(-2))/2] = (3, 0.5).

How can you show that a triangle with vertices A(2, 2), B(3, -1), and C(-3, -3) is a right triangle?

Use the distance formula to find the lengths of the sides and check if the Pythagorean theorem holds.

What does the area of a triangle with a base and height refer to in the context of the formula used?

Area = 1/2 * base * height.

How do you calculate the area of the triangle with vertices A(2, 2), B(3, -1), and C(-3, -3)?

Area = 1/2 * base * height, or using the determinant method for vertex coordinates.