Question

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 $\boldsymbol{square}$. the point $\boldsymbol{square}$ lies on $overleftrightarrow{cd}$resetnext

Explanation:

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

Slope formula: $m_{AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1$

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

Perpendicular slope: $m_{CD}=-\frac{1}{m_{AB}}=-1$

Step3: Equation of $\overleftrightarrow{CD}$

Use point-slope form: $y-y_1=m(x-x_1)$
$y-12=-1(x-5)$
Simplify: $y=-x+17$

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

Set $y=0$: $0=-x+17$
Solve for $x$: $x=17$

Step5: Verify point on $\overleftrightarrow{CD}$ (example check for a point like (8,9): $9=-8+17=9$, so (8,9) lies on it; any point satisfying $y=-x+17$ works)

Answer:

The x-intercept of $\overleftrightarrow{CD}$ is $\boldsymbol{17}$. Any point that satisfies the equation $y=-x+17$ (e.g., $\boldsymbol{(8, 9)}$) lies on $\overleftrightarrow{CD}$.