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Precalculus
Section 1.1
Q. 32
A. Plot each point on the xy-plane and form triangle ABC.
B. Show that triangle ABC is a right triangle.
C. Find its area.
Points: A= (-2, 5), B = (12, 3), C = (10, -11)
For Part A, I don't know how to upload photos to this site. Does anyone know?
For Part B, I need to use the distance formula for points on the xy-plane three times.
In other words, I must find d(A,B), d(B,C) and d(A,C). Is this correct?
For Part C, I need to use the answer to Parts A and B to find the area of triangle ABC. Is this right?
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Part (B)
Square of the distance AB is
AB^2 = + = 14^2 + 2^2 = 196 + 4 = 200.
Square of the distance BC is
BC^2 = = (-2)^2) + (-14)^2 = 4 + 196 = 200.
Square of the distance AC is
AC^2 = + = 12^2 + (-16)^2 = 144 + 256 = 400.
Thus, AC^2 = AB^2 + BC^2.
From it, you conclude that triangle ABC is a right-angled triangle.
Its sides AB and BC are the legs, while AC is the hypotenuse.
Part (C)
To find the area of triangle ABC, calculate half of the product of its legs
area = = = 100 square units.
Thus questions (B) and (C) are answered.
For (A), this site has all necessary interior tools to make a plot.
You can find all necessary info in the help and/or in examples section to this forum.
If you want to present a copy of a plot, the simplest way is to upload somewhere in
a specialized website and then provide a link to this plot in your post.
Happy learning !