GRE 504Work Sheet CRS SKILL GRE 504 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION GRE 402 Comprehend the concept of length on the number line Level 2 – MOST students will GRE 504 Find the midpoint of a line segment attain mastery of the focus skill in isolation. Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will GRE 603 Use the distance formula attain mastery of the extension GRE 605 Recognize special characteristics of circles skill. by their graph Level 1 1. Use the number line below to find the coordinate of the midpoint of each segment. a.
CE
b.
DG
c.
AF
d.
EG
e.
AB
f.
BG
g.
BD
h.
DE
2. In the diagram of collinear points, GK = 24, HJ = 10, and GH=HI=IJ. Find each length. G
a. HI b. JK H
I
c. IG J
K
d. IK 1 3. In the diagram below, C is the midpoint of BD, segment CD is 3 inches long, and segment AD is 16 inches long. Find the length of segment AB. 4. On the line below, the length of RS is 8 centimeters and the length of ST is 14 centimeters. What is the distance in centimeters from the midpoint of RS to point T? 5. Points B and C lie on AD as shown below. The length of AD is 60 units; AC is 34 units long; and BD is 46 units long. How many units long, if it can be determined, is BC? Level 2 6. Find the midpoint between each set of points. 2 7. Find the midpoint of the line segment with the given endpoints. (2,4) and (1,-­‐3) (-­‐4,4) and (-­‐2,2) (5,2) and (-­‐4,-­‐3) (-­‐1,1) and (5,-­‐5) (2,-­‐1) and (-­‐6,0) (-­‐3.1,-­‐2.8) and (-­‐4.92, -­‐3.3) Level 3 8. Coach Behringer drew his football team’s next play on a coordinate grid. He placed Avery at (1 3). He will be passing the ball to Jeremy at (6 3). In case the ball doesn’t reach Jeremy, in the previous problem, Coach Behringer placed Joel at the midpoint. Where is Joel on Coach Behringer’s grid? 9. The Lotto Mart is mapped on a coordinate grid with the origin being at the main entrance. The chocolate bar is located at the point (-­‐1, 3) and cake house is located at (1, 5). Where is the midpoint between the two points located? 10. A certain university is mapped on a coordinate grid with the origin being at the library. Math’s building is located at the point (1,5) and the History’s building is located at (4,9). Where is the midpoint between the two buildings located? If your answer has a fraction in it, leave it as a completely reduced, improper, fraction in the form “a/b”. 3 11. A triangle is located in the (x, y) coordinate plane. One side of the triangle has vertices at (3, 1) and (-­‐5,1). What are the coordinates for the midpoint of this side of the triangle? 12. . A house and a school are 5.3 miles apart on the same straight road. The library is on the same road, halfway between the house and the school. Draw a sketch to represent the situation. Mark the locations of the house, school, and library. How far is the library from the house? 13. The diagonals of parallelogram ABCD have a common midpoint. What is the midpoint of parallelogram ABCD? 6
A
4
2
B
-5
5
-2
D
-4
-6
C
14. A circle is centered at (-­‐2, 2). Segment HP has both endpoints on the circle goes through the center. If point H is located at (-­‐7,5), what are the coordinates of point P? 4 Level 4 15. Find the other endpoint of the line segment with the given endpoint and midpoint. 16. The point (-­‐8, 7) on the standard (x,y) coordinate plane is the midpoint of points (2x-­‐3, 5y-­‐7) and (4x+7, 6y+3). What is the value of x and y? 17. Point M is the midpoint of segment AB. Point A is at (3x+7, 7y-­‐1), point M is located at (2x+4, 5y-­‐5) and point B is located at (5,-­‐3). What are the coordinates of points A and M? 5 Level 5 18. Find the length (distance between end points) of the line segments below. a. The length of line segment a is 6
b
c
4
b. The length of line segment b is 2
c. The length of line segment c is -5
5
a
-2
-4
-6
19. Find the distance between each set of points. (0,-­‐2) and (-­‐5,-­‐1) (10,1) and (9,-­‐4) (6,4) and (-­‐5,-­‐1) (3,8) and (9,10) (-­‐8,10) and (-­‐6,7) (-­‐5,6) and (8,-­‐4) 6 20. For the given endpoints of a diameter, find a. the center of the circle Endpoints (-8, 6) and (0, 0)
b. the radius of the circle Center of Circle Radius of Circle (4,-9) and (-2, -9)
(-5, 7) and (4, -2)
(-2, -3) and (4, 5)
(3, 4) and (2, 1)
21. The positions of two airplanes approaching an airport are plotted on a graph grid with the airport located at (0 , 0). The locations of the planes are given by the coordinates (-­‐8, 5) and (-­‐2, 2). Each grid square is 1 mile wide. How far apart are the approaching airplanes? Round your answer to the nearest tenth of a mile. 7 o
09
o
36
22. Triangle ABC has coordinates A (3, 9), B (5,1) and C (9, 5). D is the midpoint of AB and E is the midpoint of AC. a) Graph the points A, B, and C (make sure you label them). Find the coordinates of points D and E. Show all work. D = E = b) Plot points D and point E on the graph and label. c) Find the length of DE. Show all work. Mixed Review 23. Find the value of x. G
x°
A
C
D
63°
F
E
24. Give four different names for the angle below. 8 25. Fill in the missing values. Give the distance to the nearest tenth. Points
( -5, 6) and (1, -8)
Slope
Midpoint
Distance
(3, 8) and (7 2)
(-4, -9) and (6, -2)
(-5, 4) and (-5, 8)
(1, -2) and (-9, -11)
9