Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar.
\\(\overleftrightarrow{ab}\\) and \\(\overleftrightarrow{bc}\\) form a right - angle at their point of intersection, b.
if the coordinates of a and b are (14, -1) and (2, 1), respectively, the y - intercept of \\(\overleftrightarrow{ab}\\) is
and the equation of \\(\overleftrightarrow{bc}\\) is y = x +.
if the y - coordinate of point c is 13, its x - coordinate is.

Explanation:

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

$m_{AB}=\frac{1 - (-1)}{2 - 14}=-\frac{1}{6}$

Step2: Find y - intercept of $\overleftrightarrow{AB}$

Using point - slope form with point $(2,1)$: $y - 1=-\frac{1}{6}(x - 2)$, so $y=-\frac{1}{6}x+\frac{4}{3}$, y - intercept is $\frac{4}{3}$.

Step3: Find slope of $\overleftrightarrow{BC}$

Since $\overleftrightarrow{AB}\perp\overleftrightarrow{BC}$, $m_{BC}=6$.

Step4: Find equation of $\overleftrightarrow{BC}$

Using point - slope form with point $(2,1)$: $y - 1=6(x - 2)$, so $y = 6x-11$.

Step5: Find x - coordinate of C

If $y = 13$ in $y = 6x-11$, then $13=6x-11$, $x = 4$.

Answer:

$\frac{4}{3}$; $6$; $-11$; $4$