Question

Triangle ABC is given by the points A(3, 2), B (4, 4), and C(5, 1). Select True or False for each statement.

Answer 1

Answer:

C. The perimeter of ΔABC is 7.6 units.

Step-by-step explanation:

Triangle ABC is given by the points A(3, 2), B(4, 4), and C(5, 1). Determine if each statement is True or False.

A. The perimeter of ΔABC is 9.9 units.

B. ΔABC is an equilateral triangle.  

C. The perimeter of ΔABC is 7.6 units.

Solution:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene, acute, obtuse and right angled triangle.

The distance between two points (x₁, y₁) and (x₂, y₂) in the coordinate plane is:

$Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Given the vertices of triangle ABC as A(3, 2), B(4, 4), and C(5, 1). Therefore we have to calculate the side lengths of the triangle:

$AB=\sqrt{(4-3)^2+(4-2)^2}=\sqrt{1+4}=\sqrt{5} \\\\AC=\sqrt{(5-3)^2+*(1-2)^2}=\sqrt{4+1}=\sqrt{5} \\\\BC=\sqrt{(5-4)^2+(1-4)^2}=\sqrt{1+9}=\sqrt{10}$

1) Perimeter of the triangle = AB + AC + BC = √5 + √5 + √10 = 7.6 units

2) Since only two sides of the triangle are equal (i.e. AB = AC), hence the triangle is an isosceles triangle.