Chapter 6, Problem 12CR

Solution

To calculate: The slope of chord $\overline{AC}$ and $\overline{AT}$

The slope of AC and AT are $\frac{1}{3}$ and $-3$ .

Given information: Coordinates A, T and C, are $(8,6),(10,0)$ and $(-10,0)$ is provided in the question which will help to find the solution.

Formula: Slope = $\frac{y_2-y_1}{x_2-x_1}$ .......... $\left(1\right)$

Calculation: Here, coordinates A, T and C, are $(8,6),(10,0)$ and $(-10,0)$ , putting these values in equation $\left(1\right)$

Slope of AC = $\frac{6}{18}$

➔ $\frac{1}{3}$

Now, slope of AT = $\frac{-6}{2}$

➔ $-3$

And, here $m_1\times m_2=-1$

➔ $3\times -3=-1$

Since the product of the slope is “-1”,therefore, $\Delta CAT$ is right angled triangle

Conclusion: Hence, the slope of AC and AT are $\frac{1}{3}$ and $-3$