Problema Solution
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)
Answer provided by our tutors
We will solve for thee following points:
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
From the graph we see that the point D(3, 1) lies on the circle.