Question

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AB and BC form a right angle at their point of intersection, B.
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If the coordinates of A and B are (14, -1) and (2, 1), respectively, the y-intercept of AB is
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and the equation of BC

is y= x +

If the y-coordinate of point C is 13, its x-coordinate is

Answer 1

Answer:

1. $\dfrac{4}{3}$

2. $y=6x-11$

3. $4$

Step-by-step explanation:

The equation of the line that passes trough the points A(14,-1) and B(2,1) is

$\dfrac{x-14}{2-14}=\dfrac{y-(-1)}{1-(-1)},\\ \\\dfrac{x-14}{-12}=\dfrac{y+1}{2},\\ \\y+1=-\dfrac{1}{6}(x-14),\\ \\y=-\dfrac{1}{6}x+\dfrac{7}{3}-1,\\ \\y=-\dfrac{1}{6}x+\dfrac{4}{3}.$

The y-intercept of this line is

$y=-\dfrac{1}{6}\cdot 0+\dfrac{4}{3}=\dfrac{4}{3}.$

Line BC is perpendicular to line AB, then its slope is $6.$ Line BC passes through the point B, so

$y-1=6(x-2),\\ \\y-1=6x-12,\\ \\y=6x-11.$

If the y-coordinate of point C is 13, then x-coordinate is

$13=6x-11,\\ \\6x=13+11,\\ \\6x=24,\\ \\x=4.$