Question

1. Determine whether Point D lies on the circle whose center is Point B and which contains the Point C. Show your answer algebraically and graphically. Point D (1, ); Point B (0, 0); Point C (0, 2) Point D (3,1); Point B (-1,-2); Point C (4, -2) 2. A scalene triangle is a triangle that has different side lengths. Create your own scalene triangle. Use the vertices of your triangle and the distance formula to support your answer. 3. Use the set of vertices to complete steps a-e. Quadrilateral EFGH has the vertices E(1, 3), F(2, 6), G(4, 4), and H(5, 7). Find the following information for each set of points. Graph the vertices to form quadrilateral EFGH. Determine whether the quadrilateral is a trapezoid, parallelogram, rhombus, rectangle or square. Support your conclusion mathematically Find the point of intersection for the diagonals. Calculate the slope of the diagonals. Are the diagonals perpendicular? Find the perimeter of the quadrilateral.

Answer 1

hope i helped

Explanation:

Point D (3,1); Point B (-1,-2); Point C (4, -2)

Point D lies on the circle whose center is Point B and which contains the Point C if the distance:

BD = BC

BD^2 = BC^2

(- 1 - 3)^2 + (- 2 - 1)^2 = (4 - (-1))^2 + (-2 - (-2))^2

16 + 9 = 25

25 = 25

Follows, point D lies on the circle with radii 5.

To solve graphically we first need to write the equation of the circle whose center is Point B and which contains the Point C:

(x - (-1))^2 + (y - (-2))^2 = 5^2

(x + 1)^2 + (y + 2)^2 = 5^2