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Refer to triangle ABC in the figure.
(a) Show that triangle ABC is a right triangle by using the converse of the Pythagorean Theorem.
(b) Find the area of triangle ABC.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above. To illustrate further the problem, let's label further the given figure as follows
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| Photo by Math Principles in Everyday Life |
(a) The first thing that we have to do is to get the length of each sides of a triangle using the distance of two points formula.
The length of AB is
The length of BC is
The length of AC is
Next, apply the Pythagorean Theorem by substituting the values of the sides of the triangle. Since AC is the longest side, then it is the hypotenuse of a right triangle.
Since both sides of the equation are equal, then ΔABC is a right triangle.
(b) If the vertices of a triangle are given, then we can get the area of a triangle as follows
Since the area of any plane figure is always in absolute value or positive value, then the area of a triangle is
