Answer:
Part 1 : Figure show the graph of triangle
Part 2 : The area of triangle is 4 sqaure units
Step-by-step explanation:
Given points A(1, -3), B(3, -1) and C(5, -3) make triangle.
Part 1:
Figure show the graph of triangle with A(1, -3), B(3, -1) and C(5, -3) as vertices.
Part 2: Find the area of the triangle.
The area of triangle is given by A=![\frac{(Base)(height)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28Base%29%28height%29%7D%7B2%7D)
From figure, Take base as length of AC
Length of line is given by L=![\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28X1-X2%29%5E%7B2%7D%2B%28Y1-Y2%29%5E%7B2%7D%20%7D)
Now, Base = length of AC
Base =![\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28X1-X2%29%5E%7B2%7D%2B%28Y1-Y2%29%5E%7B2%7D%20%7D)
=![\sqrt{(1-5)^{2}+((-3)-(-3))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%281-5%29%5E%7B2%7D%2B%28%28-3%29-%28-3%29%29%5E%7B2%7D%7D)
=![\sqrt{(-4)^{2}+(0)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4%29%5E%7B2%7D%2B%280%29%5E%7B2%7D%7D)
=![\sqrt{16}](https://tex.z-dn.net/?f=%5Csqrt%7B16%7D)
=4units
and Height as difference of y-component of point A and point B
Height = (y of component of point B)- (y of component of point A)
= (-1)- (-3)
= 2units
Therefore, The area of triangle is given by A=![\frac{(Base)(height)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28Base%29%28height%29%7D%7B2%7D)
A=![\frac{(4)(2)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%284%29%282%29%7D%7B2%7D)
A=4 sqaure units