CLASSIFYING TRIANGLES BY COORDINATES WORKSHEET

The vertices of a triangle are given. Classify the triangle as scalene, isosceles, or equilateral.

Problem 1 :

(-5, 0), (0, 6), (5, 0)

Solution

Problem 2 :

(0, -3), (0, 3), (3, 0)

Solution

Problem 3 :

(-2, 5), (1, -1), (4, 6)

Solution

Problem 4 :

(1, 4), (4, 1), (7, 4)

Solution

Problem 5 :

(-1, -6), (1, 1), (4, -5)

Solution

Problem 6 :

(-4, 3), (2, -1), (8, -1)

Solution

Problem 7 :

The coordinates of the vertices of triangle ABC are A(-5, 3), B(-1, -2) and C(2, 3). Show that triangle ABC is scalene.

Use the distance formula to classify triangle ABC, as either equilateral, isosceles or scalene :

Problem 1 :

A(3, -1), B(1, 8), C(-6, 1)

Solution

Problem 2 :

A(1, 0), B(3, 1), C(4, 5)

Solution

Problem 3 :

A(-1, 0), B(2, -2), C(4, 1)

Solution

Problem 4 :

A(√2, 0), B(-√2, 0), C(0, -√5)

Solution

Problem 5 :

A(√3, 1), B(-√3, 1), C(0, -2)

Solution

Problem 6 :

A(a, b), B(-a, b), C(0, 2)

Solution

Problem 1 :

Find the area of a triangle whose vertices are (3, 0), (7, 0) and (8, 4).

Solution

Problem 2 :

The area of a triangle whose vertices are (5, 0), (8, 0) and (8, 4) (in sq.units) is 

A) 20    B) 12    C) 6

Solution

Problem 3 :

The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is (7/2, y), find the value of y.

Solution

Problem 4 :

Find the values of k so that the area of the triangle with vertices (1, -1), (-4, 2k) and (-k, -5) is 24 sq. units.

Solution

Problem 5 :

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are A(2, 1), B(4, 3) and C(2, 5).

Solution

Problem 6 :

For what type of k, (k > 0), is the area of the triangle with vertices (-2, 5), (k, -4) and (2k + 1, 10) to 53 sq. units?

Solution

Problem 1 :

Find the area of the triangle ABC with A(1, -4) and the mid-points of sides through A being (2, -1) and (0, -1).

Solution

Problem 2 :

Find the value of m if the points (5, 1), (-2, -3) and (8, 2m) are collinear.

Solution

Problem 3 :

Find the area of the triangle whose vertices are (-8, 4), (-6, 6) and (-3, 9)

Solution

Problem 4 :

The points A(2, 9), B(a, 5) and C(5, 5) are the vertices of a triangle ABC right angles at B. Find the values of a and hence the area of ΔABC.

Solution

Problem 5 :

A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ΔADE

Solution

Problem 1 :

Name the type of triangle formed by the points A(-5, 6), B(-4, -2) and C(7, 5) 

Solution

Problem 2 :

Find the coordinates of the point Q on the x axis which lies on the perpendicular bisector of the line segment joining the points A(-5, -2) and B(4, -2). Name the type of triangle formed by the points Q, A and B.

Solution

Problem 3 :

If the vertices of triangle ABC are A(-2, 4), B(-2, 8) and C(-5, 6) then triangle ABC is classified as 

a) right        b)  scalene      c)  isosceles      d)  equilateral

Solution

Problem 4 :

Triangle ABC has vertices with A(x, 3), B(−3, −1), and C(−1, −4). Determine and state a value of x that would make triangle ABC a right triangle. Justify why ABC is a right triangle. [The use of the set of axes below is optional.]

Solution

Related Pages

• Classify the triangles by its angle measures
• Classify the triangles by its side length
• Properties of triangles worksheet
• Order the sides of the triangle from shortest to longest worksheet
  
• Find the missing side of right triangle