Try this beautiful problem from Geometry based on the area of the triangle.
What is the area of the triangle formed by the lines $y=5$, $y=1+x$, and $y=1-x$
Geometry
Triangle
Linear equation
But try the problem first...
Answer: $16$
AMC-8 (2019) Problem 21
Pre College Mathematics
First hint
Find the three vertex of the triangle
Can you now finish the problem ..........
Second Hint
The area of the Triangle =\(\frac{1}{2} \times \{x_1(y_2 - y_3)+x_2(y+3 -y_1)+x_3(y_1 -y_2)\}\)
can you finish the problem........
Final Step
Solving two The lines y=5 and y=1+x are intersect at (4,5)=\((x_1,y_1)\)(say)
Solving two The lines y=5 and y=1-x are intersect at (-4,5)=\((x_2,y_2)\)(say)
Solving two The lines y=1-x and y=1+x are intersect at (0,1)=\((x_1,y_1)\)(say)
Then the area of Triangle =\(\frac{1}{2} \times\{ x_1(y_2 - y_3)+x_2(y+3 -y_1)+x_3(y_1 -y_2)\}\)
= \(\frac{1}{2} \times \{4(5-1)+(-4)(1-5)+0(5-5)=\frac{1}{2} (16+16)=16\}\)
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