Question

1. find the center of the circle that can be circumscribed about the triangle.

(-1, -1)
(-4, 0)
(-2, -3)
(0, 0)

Explanation:

Step1: Recall circum - center property

The circum - center of a right - angled triangle is the mid - point of the hypotenuse.

Step2: Identify the right - angled triangle and hypotenuse

From the graph, we can see that the triangle is a right - angled triangle. The endpoints of the hypotenuse are $(-4,0)$ and $(0, - 6)$.

Step3: Use mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-4,y_1 = 0,x_2 = 0,y_2=-6$.
\[

$$\begin{align*} x&=\frac{-4 + 0}{2}=-2\\ y&=\frac{0+( - 6)}{2}=-3 \end{align*}$$

\]

Answer:

$(-2,-3)$