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

1.
`(4)/(3)`

2.
`y=6x-11`

3.
`4`

Explanation:

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

`(x-14)/(2-14)=(y-(-1))/(1-(-1)),\\ \\(x-14)/(-12)=(y+1)/(2),\\ \\y+1=-(1)/(6)(x-14),\\ \\y=-(1)/(6)x+(7)/(3)-1,\\ \\y=-(1)/(6)x+(4)/(3).`

The y-intercept of this line is

`y=-(1)/(6)\cdot 0+(4)/(3)=(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.`