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How do you find the length of the line segment of y equals 8 -x that connects the curve of y equals x squared plus 4x plus 2 at two points?
Wiki User
∙ 13y ago
y = 8 - x
y = x2 + 4x + 2
Put the two equations equal to one another to determine the value(s) for x where the line crosses the curve.
8 - x = x2 + 4x + 2 , then x2 + 5x - 6 = 0
This can be factored
x2 + 5x - 6 = (x + 6)(x - 1) = 0
Then either x + 6 = 0, which means x = -6 and thus y = 8 - x = 8 -(-6) = 14
Or, x - 1 = 0, which means x = 1 and thus y = 8 - x = 8 - 1 = 7
The line segment is between points (-6,14) and (1,7)
The length of the segment = √[(x1 - x2)2 + (y1 - y2)2]
= √[(-6 -1)2 + (14 - 7)2]
= √[(-7)2 + 72] = √[49 + 49] = √98 = 7√2 = 9.8995 (4dp)
Wiki User
∙ 13y ago
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