Name:
Date:
Secondary Math I – 15.1: Classifying Triangles on the Coordinate Plane
Period:
Mr. Heiner
Determine the location (give a coordinate pair) of point C such that triangle ABC has each given characteristic. The
graph shows line segment AB.
Ex. Triangle ABC is a right triangle.
Point C can have an infinite number of locations as long
as the location satisfies one of the following
conditions:
 Point C could be located anywhere on the line
𝑦 = 3 except at 𝑥 = 2.
 Point C could be located anywhere on the line
𝑦 = −3 except at 𝑥 = 2.
1. Triangle ABC is an acute triangle.
2. Triangle ABC is an obtuse triangle.
3. Triangle ABC is an equilateral triangle.
4. Triangle ABC is a scalene triangle.
5. Triangle ABC is an isosceles triangle.
Graph Triangle ABC using each set of given points. Determine if ABC is scalene, isosceles, or equilateral.
Ex. 𝐴(−3,1), 𝐵(−3, −3), 𝐶(1,0)
6. 𝐴(8,5), 𝐵(8,1), 𝐶(4,3)
𝐴𝐵 = 1 − (−3) = 4
Using the Distance Formula:
𝐵𝐶 = √16 + 9 = √25 = 5
𝐴𝐶 = √16 + 1 = √17
Since all sides are different lengths, ∆𝐴𝐵𝐶 is scalene.
7. 𝐴(5,8), 𝐵(5,2), 𝐶(−3,5)
8. 𝐴(−2, −6), 𝐵(6, −6), 𝐶(2, −3)
9. 𝐴(0,0), 𝐵(4,0), 𝐶(3,7)
10. 𝐴(−6,4), 𝐵(0,4), 𝐶(−2, −2)
Graph Triangle ABC using each set of given points. Determine if ABC a right, acute, or obtuse triangle.
Ex. 𝐴(0,4), 𝐵(4,5), 𝐶(1,0)
11. 𝐴(−6,1), 𝐵(−6, −4), 𝐶(4,0)
Using the Slope Formula:
1
5
The slope of AB: 4, The slope of BC: 3, and
the slope of AC: −4
1
Since 4 (−4) = −1, this is a right triangle.
12. 𝐴(−5,7), 𝐵(7,7), 𝐶(1,4)
13. 𝐴(−4, −1), 𝐵(1,3), 𝐶(3, −4)
14. 𝐴(2,6), 𝐵(8, −3), 𝐶(2, −7)
15. 𝐴(−2,6), 𝐵(6, −3), 𝐶(0,0)
16. The following grid shows a map of Stoneville and the locations of several businesses in the town. A line segment
has been drawn between the locations of the mall and the diner. Using this line segment as one side of a triangle,
determine the business (or businesses) whose location, when connected with the line segment, would result in each
of the following types of triangles.
a. an isosceles triangle
b. an acute triangle
c. a scalene triangle
d. a right triangle
e. an equilateral triangle
f. an obtuse triangle