Task on Triangles in the Coordinate Plane
Name_________________________
For the entirety of this assignment, a straightedge must be used or points will be deducted.
Suppose that triangle RST has vertices located at R(-4, 0), S(-1, 5), and T(3, 2).
1.
Plot the vertices on the coordinate plane provided on the answer sheet. In addition,
connect the vertices to form the triangle. Label the vertices with the appropriate letter.
2.
What are the coordinates of the midpoint of side RS ?
3.
What are the coordinates of the midpoint of side ST ?
4.
What are the coordinates of the midpoint of side RT ?
5.
Plot everything in Question 1 again - also plot the midpoints of the three sides.
Clearly mark the midpoints with solid dots.
--------------------------------------------------------------------------------------------------------------------If you recall, a median of a triangle is a segment that joins a vertex to the midpoint of the
opposite side.
A new triangle has been graphed on the coordinate plane on this worksheet as well as the answer
sheet. The midpoints of its sides have been clearly indicated with dots.
6.
6
Draw the three medians for the given triangle on
the answer sheet.
4
7.
The three medians intersect at one point called
the centroid. What are the coordinates of the
centroid of the given triangle?
2
5
--------------------------------------------------------------------------------------------------------------------Consider the triangle graphed below. All three medians have been constructed, and they
intersect at the centroid (point C).
8.
Consider the median from point R.
6
A)What is the distance from the vertex (R) to
the centroid (C)?
B)What is the distance from the centroid to
the midpoint of the opposite side (r)?
9.
r
T
S
4
C
2
s
t
Consider the median from point S.
5
A)What is the distance from the vertex (S) to
the centroid (C)?
R
-2
B)What is the distance from the centroid (C) to the midpoint of the opposite side (s)?
10.
Fill in the blank: The distance from the vertex to the centroid is ____________________
times the distance from the centroid to the midpoint of the opposite side.
Your answer will be a number. You should use #8 and #9 to answer this question.
More Practice with Shapes in the Coordinate Plane
Name_________________________
Classify the triangle or quadrilateral plotted on the coordinate plane with the given vertices.
Prove the classification.
1. Quadrilateral ABCD with vertices at
A(1, 2), B(2, 1), C(3, 2) and D(2, 3)
3. Quadrilateral HJKL with vertices at
H(2, 7), J(1, 0), K(-4, -5), and L(-3, 2)
2. Triangle EFG with vertices located at
E (-4, 5), F(6, 5), and G(1, -4)
4. Quadrilateral MNPQ with vertices at
M(-2, 2), N(2, 2), P(5, -4), and Q(1, -4)
Task on Triangles in the Coordinate Plane
1.
Name_________________________
6.
6
6
4
4
2
2
5
5
2.________________________
7._________________________
3.________________________
8. A)______________________
4.________________________
B)______________________
9. A)_____________________
B)_____________________
10. ________________________
5.
6
4
2
5