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Geometry / Mr. Hansen |
Name: __________________________ |
Coordinate Geometry Worksheet
I. Carefully sketch each of these graphs and provide other information as required.
1. 3x - y = 3
a) Sketch:
b) Write the coordinates of the y-intercept: _________________
c) Write the coordinates of the x-intercept: _________________
2. x + y = 25
a) Sketch:
b) Write the coordinates of the x-intercept: _________________
c) Write the slope: _______________
d) Write the value of x when y=23: ________________
e) Write the coordinates of the point where this line crosses the perpendicular bisector of the segment connecting (-1,3) and (7, -4).
3.. Sketch the set of points satisfying both inequalities:
2x + y < 4
y < 3x+1
II. Plot these points and label each with the correct letter:
A = (2, 3) B = (5, 12) C = (10, 5)
1. Draw triangle ABC.
2. Write the coordinates of the midpoint of sAC.
3. Find the length, correct to the nearest hundredth, of the median from B to sAC.
4. Write a correct equation for the line which contains the altitude from B to sAC.
5. Find the area of triangle ABC.
III. Matching:
Write the letter of the correct equation in the blank to the left of the description of its graph.
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_____ 1) line through (2, 5) and (4, 5) |
a) x - y = 5 |
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_____ 2) line through (5, 2) and (5, 4) |
b) x + y = 5 |
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_____ 3) line through (0, 5) and (5, 0) |
c) y - x = 5 |
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_____4) line through (0,-5) and (5, 0) |
d) y = x |
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_____5) line through (0, 0) and (5, 5) |
e) x = 5 |
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f) y = 5 |
IV. Complete each of these problems.
1. Write the equation of a line which has a graph which is parallel to the line y - 2x = 8
and contains the point (5, 5).
2. The graphs of the lines x + 2y = 5 and x - 4y = -16 intersect in exactly one point.
What are the coordinates of this point? __________________
V. Sketch the graph of a circle with center at the origin and the point (5, 12) on the graph.
Now add a line tangent to that circle at the point (5,12). What is its slope? _____________
a) Write a correct equation for the graph of the circle.
b) Write a correct equation for the line tangent to the circle at (5, 12).
VI. Given the coordinates in space of these points: P = (2, 3, -1) and Q = (6, 11, 5)
1. Write the coordinates of M, the midpoint of sPQ.
2. Write the exact length of the line segment sPQ.