Math 3A Cycle 4 Analytical Geometry

1
Math 3A Cycle 4Analytical Geometry

• Review Activity

2
Distance, Mid-Point, Slope
Analytical Proof
Name That Point
Applications Maps
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3

10 points

Find the slope of a line through the points
A(2,5) and B(0,9).


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4
A N S W E R
10 points
-4
rise
5-9

Slope

-2


run
2
2-0
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5

20 points
What is the distance from C to D?
D(0,2)
C(-6,0)
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6
A N S W E R
20 points
62 22 c2
36 4 c2
40 c2
40 c
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7

30 points
If (4,-2) is a mid-point of the line segment from
L(0,1) to M, then find the coordinates for point
M.
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8
A N S W E R
30 points
M must be (8,-5)
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9

10 points
Which coordinate geometry formulas provide the
evidence to guarantee a quadrilateral must be an
isosceles trapezoid?
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10
A N S W E R
10 points
Slope formula 4 times to show 1 pair of opposite
sides are parallel and the other pair are not.


Distance formula 2 times to show the unparallel
sides are equal in length.
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11

20 points
The CEI Method is used to create a proof in
analytical geometry. What does it stand for and
what is the meaning of each step?
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12
A N S W E R
20 points
Claim-What do you believe to be true?
Evidence-What formulas and work supports your
claim?

Interpretation-How does the evidence guarantee
the truth of your claim?
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13

30 points
Below is a part of a proof intending to show DABC
is a right triangle. What is the last step?
C / ABC is a right angle
E Slope AB 2/3 Slope BC -3/2
I
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14
A N S W E R
30 points
I Since the slopes of AB BC are negative
reciprocals, they must be perpendicular to each
other, and therefore, they will make a right
angle at B.
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15

10 points

Knowing 3,4,5 is a pythagorean triple, name any
first quadrant point exactly 5 units from P(2,3)
and whose x value isnt 2 and whose y value isnt
3.
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16
A N S W E R
10 points
B(5,7)
Either (5,7) or (6,6) would be correct answers.
3

A(6,6)
4
P(2,3)
3
4
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17

20 points
M is the mid-point of both segments AB CD. If
A(1,1), B(7,3), and C(0,0) are given, Find the
coordinates for D.
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18
A N S W E R
20 points
Since the mid-point M of AB must be (4,2), this
means M(4,2) will also be the mid-point of CD.
So end point D must be (8,4).

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19
30 points
A line passes through the point (-4,-8) and has a
slope of 3. Between what two integers is its x
intercept and name the point at which it crosses
the y axis.

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20
A N S W E R
30 points
y
Crosses the x axis between -2 -1
Crosses the y axis at (0,4)

1
3
1
3
X
1
3
1
3
(-4,-8)
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21

10 points
The slope of the line from Boston to Gloucester
is 1. Given the distance north of Boston to
Middleton Colony is 48 miles, what is the
distance from Boston and Gloucester?
48
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22
A N S W E R
10 points
48
482482c2 4608 c2 67.9 miles c

48
c
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23

20 points
Each side of the square on the grid is 17 miles.
Find how far it is from Rochester to Ithaca?
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24
A N S W E R
20 points
3242c2 25 c2 5 c

5 x 17miles 85 miles from Rochester to Ithaca.
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25

30 points
C
Find the slope of BA and the slope of AC. What
do you notice?
A
B
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26
A N S W E R
30 points
Slope of BA 3/9 Slope of AC -9/3
They are negative reciprocals. This means they
will make a right angle.
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