Question

What is the area of the triangle formed by the lines $y=5,$ $y=1+x,$ and $y=1-x?$

$4$

$8$

$10$

$12$

$16$

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First, let us find the vertices of the triangles. The intersections between $y = 5$ and the other two lines are $(4, 5) \text{ and } (-4, 5).$

To find the third intersection, we can equate the two equations to get $1 + x = 1 - x \Rightarrow x = 0.$

This gives us the point $(0, 1).$

Note that the first two intersection points are mirrored across the $y$ -axis. This tells us that the triangle is isosceles.

The base is therefore $2 \cdot 4 = 8,$ and the height is $5 - 1 = 4.$ The area of the triangle is therefore $\dfrac{1}{2} \cdot 8 \cdot 4 = 16.$

Thus, the correct answer is E.