Question

select the correct answer from each drop - down menu. cd is perpendicular to 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 cd is <multiple - choice options: (12, 0), (15, 0), (17, 0), (19, 0)>. the point lies on cd.

Explanation:

Step1: Find slope of 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 slope of CD

Since $CD\perp AB$, the product of their slopes is - 1. If $m_{AB}=1$, then $m_{CD}=-1$.

Step3: Write the equation of line CD

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using 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

To find the x - intercept, set $y = 0$. So, $0=-x + 17$, which gives $x = 17$. The x - intercept of $CD$ is $(17,0)$.

Answer:

$(17,0)$