Unit #9: Coordinate Geometrymisszsgeometrysupport.weebly.com/uploads/5/7/2/1/5721341/unit_9... ·...
Transcript of Unit #9: Coordinate Geometrymisszsgeometrysupport.weebly.com/uploads/5/7/2/1/5721341/unit_9... ·...
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Unit #9: Coordinate Geometry
Trapezoids
Coordinate Geometry Tool Box
Midpoint
Distance
Coordinate Geometry Proof
Unit #9 Test Review
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Name:__________________ Day ___ Per ___
Geometry Lab Trapezoids
1) Using the word box, label the diagram below:
2) Things to know about an Isosceles Trapezoid:
Leg Base Median
The Median (aka mid-segment):
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3) In isosceles trapezoid ABCD, AB|| DC. If AD = 3x + 4 and BC = x + 12,
solve for x.
4) If RT is the median of trapezoid ABCD. Find the length of RT.
5) In the accompanying diagram, isosceles trapezoid CDEF has bases of
lengths 6 and 12 and an altitude of length 4. Find CD.
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6) In trapezoid ABCD, AB||CD. If AB = 2 and CD = 50, what is measure
of the median MN?
7) Find the length of the median of a trapezoid if the lengths of the two
bases are 20 and 46 inches.
8) In isosceles trapezoid RSTU, RS = 8x + 5 and TU = 2x +29. Express
the length of the median QP in terms of x. (Hint: Draw a picture)
9) In isosceles trapezoid ABCD, diagonal AC is 2x+10 and diagonal
BD is 86+x. Find the length of each diagonal.
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10) In isosceles trapezoid DEGF, DE = 20, FG = 30 and DH = 12. Find the
length of GD.
11) EF is the mid-segment of trapezoid ABCD. EF = 25 and AD = 40.
Find BC.
12) Find the mR. 13) Find W.
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Coordinate Geometry Tool Box
Slope Formula:
Used to show:
Distance Formula:
Used to show:
Midpoint Formula:
Used to show:
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Name: __________________________________ Day __ Per __
Geometry Lab Coordinate Geometry-Midpoint
Midpoint Formula: (Use when you are given the two end points)
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Use when given ONE endpoint and the Midpoint: Ex:
1. Find the midpoint of the segment
connecting the points (6,4) and (3,-4).
2. The coordinates of A are (9,2) and the coordinates of G are (3,14). What are the coordinates of the midpoint of AG?
3. What is the midpoint of the line
segment that joins points (4,2) and
(2,5)?
4. Find the midpoint of the segment
connecting the points (a,b) and (3a,c).
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5. Line segment AB has endpoints A(2,3) and B(4,6). What are the coordinates of the midpointof AB?
6. A line segment has endpoints A(7,-1) and
B(-3,3). What are the coordinates of
the midpoint of AB?
7. In circle O, diameter RS has endpoints
R(3a, 2b-1) and S(a-6, 4b+5). Find the
coordinates of point O, in terms of a
and b. Express your answer in simplest
form.
8. M is the midpoint of AB . The
coordinates of A are (-2,3) and the
coordinates of M are (1,0). Find the
coordinates of B.
9. M is the midpoint of AB. If the
coordinates of A are (-1,5) and the
coordinates of M are (3,3), what are the
coordinates of B?
10. A line segment on the coordinate plane
has endpoints (2,4) and (4,y). The
midpoint of the segment is point (3,7).
What is the value of y?
11. The midpoint M of line segment AB has
coordinates (-3,4). If point A is the
origin, (0,0), what are the coordinates
of point B?
12. The coordinates of the midpoint of AB
are (2,4) and the coordinates of point B
are (3,7). What are the coordinates of
point A?
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Name: _________________________ Day __ Per __
Geometry Lab Coordinate Geometry-Distance
Distance Formula:
1. The coordinates of point R are (-3,2) and the coordinates of point T are
(4,1). What is the length of RT?
2. What is the length of the radius of a circle whose diameter has end points
of (1,0) and (5,4)?
3. Find the length of the line segment whose endpoints are (-3, 4) and (5,4).
4. Determine the length of if the coordinates of A are ( 2,-3) and of B(
2,7).
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5. is the diameter of a circle with coordinates M(7,-2) and Z(1,5). Find the
length of the radius .
6. What is the length of the line segment whose endpoints are (1, -4) and (9,2)?
7. If the endpoints of AB are A(-4,5) and B(2,-5), what is the length of AB?
8. What is the distance between points A(7,3) and B(5,-1)?
9. The coordinates of point R are (-3,2) and the coordinates of point T are (4,1). What is the length of RT ?
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Name: _________________________________ Day __ Per __ Geometry Lab Coordinate Geometry
Proofs in Coordinate Geometry
1. Determine the distance between point A(-1,-3) and point B(5,5). Write an
equation of the perpendicular bisector of AB?
2. Determine the distance between point M(-3,8) and point Z(7,-2). Write an
equation of the perpendicular bisector of MZ.
3. Given: Trapezoid MATH M(-2,3), A( 4,3), T(6,1) and H(-4,1) find the length
of the mid-segment .
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4. The vertices of ABC are A(-7, 1), B(5, -3) and C(-3,5). Prove ABC is a
right .
5. Given: A(1,6),B(7,9),C(13,6), and D(3,1) Prove: ABCD is a trapezoid
6. Prove that A(-2,2), B(1,4), C(2,8) and D(-1,6) is a parallelogram.
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7. Prove: F(-4,1), O(2,5), U(4,2), R(-2,-2) is a rectangle.
8. Given: J (4,1), E (2,3), N (2,1) Prove: JEN is an isosceles right triangle.
9. Prove that A(-3,2), B(-2,6), C(2,7) and D(1,3) is a rhombus.
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Name: _____________________________________ Day ___ Per ___ Geometry Lab Unit #9 Test Review
1) M is the midpoint of line segment TP. The coordinates of P are (-8, 4) and the
coordinates of M are (-1,-2). Find the coordinates of T.
2) Circle O has a center at (3,-5) and a diameter AB. If the coordinates of A are (-3,6),
what are the coordinates of B?
3) Find the midpoint of the segment connecting the points (4, 8) and (-2,1).
4) Find the midpoint of the segment connecting the points (3M,3E-1) and (M-6, 5E +4)
5) In circle O, diameter RS has endpoints R(3a, 2b-1) and S(a-6, 4b+5). Find the
coordinates of point O, in terms of a and b. Express your answer in simplest form.
6) Determine the perimeter of a square, whose side measures 12 . Express your
answer in simplest radical form.
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7) Find the perimeter of a rhombus, whose side measures 3 20 ( Express your answer
in simplest radical form).
8) What is the length of the line segment that joins points (6,-2) and (9,4)? Express your answer in simplest radical form.
9) Determine the distance between points G (-4,7) and Z(-7,5).
10) Find the distance between point A(-9,-6) and Z(6,3). (Round your answer to the nearest tenth.)
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11) In isosceles trapezoid ABCD AB//DC. If AD = 3x+4 and BC = x+12, find the length of AD.
12) A. Find the length of RT. B. Given isosceles trapezoid ABCD, find the height of the trapezoid.
13) In isosceles trapezoid ABCD, AB // CD, AB = 18, CD = 26 and AD = 5. Find the
length of the altitude of ABCD.
14) A. In triangle MAP, the slope of MA = -3
4. B. In triangle BOY, the slope of the
Determine the slope of the altitude altitude from vertex O to BY is 5. from vertex P to MA. What is the slope to BY?
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15) Write the equation of the perpendicular bisector of C(-5,2) and D(1,5).
16) Write the equation of the perpendicular bisector of T(4,2) and Y(-4,4).
17) Quadrilateral LOVE has vertices L(2,2), O(5,2), V(6,-2), and E(3,-2). Prove quadrilateral LOVE is a parallelogram.
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18) Quadrilateral SONG has vertices S(2,3), O(10,3), N(10,-1), and G(2,-1). Prove
quadrilateral SONG is a rectangle.