1.)
A circle has 2 chords: AB with coordinates A ( 2, 6 ) , B ( -2, 2 )
and chord CD with coordinates C ( 2, -2 ) ,
D ( 6, 2 ). Find the coordinates of the centre of the circle. Use graph
paper.
2.) Write the converse of the following statement: if 2 chords on a
circle are equal distances
( equidistant ) from the centre of the circle, then they
are congruent.
3.) Given: figure ABCD with coordinates A (-1, -6 ), B ( 5, 3
), C ( 11, -1 ) and D ( 5, -10 ).
a. Prove ABCD is a rectangle
b. Prove distance CD is 1.5 times distance AD
c. Find the midpoints of each side of the rectangle.
4.) Line segment AB has coordinates, A ( 1, 3 ), B ( 3, 4 ). Meanwhile
line segment CD has coordinates,
C ( 3, -1 ), D ( 7, y ). The two line segments are parallel. Find the
value of y.
5.) Line segment AB has coordinates, A ( 1, 3 ), B ( 3, 4 ). Meanwhile
line segment EF has coordinates,
E ( -3, 1), F ( x, -3). The two line segments are perpendicular. Find
the value of x.
*6.) Find the equation of a circle that has a centre of ( 3, -5 ) and
radius = 5 units. Express your answer in
a. standard form b. transformational
form
*7.) The following equation is for an ellipse: 4x2 + 9y2
- 16x + 90y + 205 = 0
a. Put the equation in transformational form.
b. State......
- the semi major axis and the major axis
- the semi minor axis and the minor axis.
- the centre
*8.) Put the following equation in standard form. Is this equation for
a circle or an ellipse?
x2+
y2 + 6x - 4y - 12 = 0
__________________
Answers:
1.) centre is ( 2, 2 )
2.) If 2 chords on a circle are congruent, then they are equidistant
from the centre of the circle.
3 .) a. slope AB = 3/2, slope BC = -2/3, slope CD = 3/2 and slope
DA = -2/3. The definition of a rectangle is a four sided figure with
four 90 degree angles. In ABCD, connecting sides have negative reciprocal
slopes. Therefore ABCD has four 90 degree angles and is a rectangle.
b. distance CD = 10.8 units. Distance AD is 7.2 units. CD / AD = 10.8
/ 7.2 = 1.5 times
c. midpoint of AB is ( -2, -1.5 ), midpoint of BC is ( 8, 1 ), midpoint
of CD is ( 8, -5.5 ),
midpoint of DA is ( 2, -8 )
4.) y = 1
5.) x = -1
6.) a. standard form: ( x - 3 )2 + ( y + 5 )2
= 25
b transformational form: [1/5 ( x - 3 )]2 + [ 1/5 ( y + 5
)]2 = 1
7.) [ 1/3 ( x - 2 )]2 + [ 1/2 ( y + 5 )]2 = 1
- the semi major axis is horizonatl and equals 3 units
- the major axis is horizontal and equals 6 units
- the semi minor axis is vertical and equals 2 units
- the minor axis is vertical and equals 4 units
- the centre is ( 2, -5 )
8.) ( x + 3 )2 + ( y - 2 )2 = 25 . This is a circle
becuase there is not a major and minor axis. The radius is 5 units.
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