COORDINATE GEOMETRY – CIRCLES AND CHORDS
Chord – a line segment that connects any two points on the edge of a circle
A circle contains two chords, GH and JK, with endpoints G(-10, 4), H(-2, 16), J(8, 16), K(16, 4).
A) Plot and label the four points, then use a ruler to draw the two chords … i.e. connect G&H and J&K.
(don’t draw the circle yet)
B) Write the coordinates of the midpoint of each chord. Mark these midpoints on your diagram.
(label them A and B)
C) Calculate the slope of each chord.
D) The perpendicular bisector of chord GH passes through the point _______ and has a slope of _______.
The perpendicular bisector of chord JK passes through the point _______ and has a slope of _______.
*Draw these perpendicular bisectors on your diagram. (label these lines 1 and 2)
E) Determine the equation of each new line, 1 and 2, from part (D).
1: _____________________________ 2: _____________________________
F) Mark the point of intersection of these two lines with the letter O. Write the coordinates of this point.
G) Calculate the lengths of OG, OH, OJ, and OK. What do these lengths tell you about point O?
H) Use a compass (or a steady hand) to draw the circle on the graph.