Question

11
select the correct answer from each drop - down menu.
$overleftrightarrow{cd}$ is perpendicular to $overleftrightarrow{ab}$ and passes through point c(5, 12).
if the coordinates of a and b are (-10, -3) and (7, 14), respectively, the x - intercept of $overleftrightarrow{cd}$ is. the point lies on $overleftrightarrow{cd}$.

Explanation:

Step1: Find the slope of $\overleftrightarrow{AB}$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-10,-3)$ and $B(7,14)$, $m_{AB}=\frac{14 - (-3)}{7-(-10)}=\frac{14 + 3}{7 + 10}=\frac{17}{17}=1$.

Step2: Find the slope of $\overleftrightarrow{CD}$

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of $\overleftrightarrow{CD}$ be $m_{CD}$. Since $m_{AB}\times m_{CD}=-1$ and $m_{AB} = 1$, then $m_{CD}=-1$.

Step3: Find the equation of $\overleftrightarrow{CD}$

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $C(5,12)$ and $m=-1$, we have $y - 12=-1(x - 5)$, which simplifies to $y-12=-x + 5$ or $y=-x+17$.

Step4: Find the x - intercept of $\overleftrightarrow{CD}$

To find the x - intercept, set $y = 0$. Then $0=-x + 17$, so $x = 17$.

Step5: Check which point lies on $\overleftrightarrow{CD}$

Let's assume we have points to check. Substitute the x and y values of the point into the equation $y=-x + 17$. For example, if we have a point $(x_0,y_0)$, we check if $y_0=-x_0+17$.

Answer:

The x - intercept of $\overleftrightarrow{CD}$ is $17$. (The second part about the point that lies on $\overleftrightarrow{CD}$ is incomplete in the problem statement, but if we had options we would substitute values into $y=-x + 17$ to check).