Question

triangle abc is on a coordinate - plane. segment ab is on the line y = 2 and is 6 units long. point c is on the line x=-3. if the area of △abc is 6 square units, then find a possible y - coordinate of point c.

Explanation:

Step1: Recall area formula for triangle

The area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base is the length of segment $AB$, and the height is the perpendicular distance from point $C$ to the line $y = 2$. Given $AB = 6$ and $A=6$.

Step2: Substitute values into area formula

We know $A = 6$, $base=AB = 6$. Substituting into $A=\frac{1}{2}\times base\times height$, we get $6=\frac{1}{2}\times6\times h$.

Step3: Solve for height $h$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times6\times h = 3h$. Then, solve $6 = 3h$ for $h$. Divide both sides by 3, we have $h = 2$.

Step4: Find possible $y$ - coordinates of point $C$

Point $C$ is on the line $x=-3$. The line $AB$ is on $y = 2$. The perpendicular distance from point $C$ to the line $y = 2$ is 2. So, if the $y$ - coordinate of the points on $AB$ is 2, then $y_C=2 + 2=4$ or $y_C=2-2 = 0$.

Answer:

4 or 0