VERIFYING GEOMETRIC PROPERTIES OF TRIANGLE USING ANALYTIC GEOMETRY

Problem 1  :

The vertices of a triangle are K(2, -6), L(4, 10) and M(8, -2). Let P be the midpoint of KL and Q be the midpoint of LM. Verify that :

a) PQ is parallel to KM

b) PQ is half the length of KM.

Solution

Problem 2 :

Given ∆ABC with vertices A(-7, 3), B(-2, -3) and C(4, 2).

a) Classify the triangle by side length

b) Verify that one median of the triangle is perpendicular to one of the sides.

Solution

Problem 1 :

Is ∆PQR a right angled triangle if P(1, 2), Q(5, -1) and R(-4, -4) ?

Solution

Problem 2 :

Classify  ∆DEF following triangle as scalene, isosceles or equilateral if D(5, 2), E(-3, 4) and F(-2, -3).

Solution

Problem 3 :

Given the points X(1, 4), Y(-2, 2) and Z(3, 1). Verify that ∆XYZ is a right triangle.

Solution

Problem 4 :

A triangle has vertices K(-2, 2), L(1, 5) and M(3, -3). Verify that :

a) The triangle has a right angle.

b) The midpoint of the hypotenuse is the same distance from each vertex.

Solution

Problem 5 :

A triangle has vertices U(5, 5), V(1, -3) and W(-3, -1). Verify that :

a) ∆UVW is a right triangle

b) The median from the right angle to the hypotenuse is half  as long as the hypotenuse.

Solution