Exercise 3 Page 306

Notice that the triangle is isosceles.

T(2a,0)

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We are given the following triangle on a coordinate plane.

Since T is on the x-axis, its y-coordinate must be 0. Now, recall the classification of triangles.

Classification of Triangles
Scalene Triangle	A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle	An isosceles triangle is a triangle that has two congruent sides and two base angles with the same measure.
Equilateral Triangle	An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle	An acute triangle is a triangle where all angles are less than 90^(∘) or π2.
Obtuse Triangle	An obtuse triangle is a triangle with exactly one an angle whose measure is greater than 90^(∘) or π2.
Right Triangle	A right triangle is a specific type of triangle that contains one angle of 90^(∘).

Notice that RS≅ TS. This implies that △ RST has two congruent sides. Therefore, it is an isosceles triangle. As we can see in the diagram, O(0,0) is the midpoint of the base RT. Therefore, the x-coordinate of T is the same distance from O as R is.

In conclusion, the coordinates of T are ( 2a, 0).

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