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Brut [27]
3 years ago
9

↔ ↔

Mathematics
1 answer:
MrRissso [65]3 years ago
7 0

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.

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