Parallel lines
Geometry
Level
2
Find the number of lines that are parallel to and have an intercept of 10 units between the coordinate axes.
The answer is 2.
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1 solution
y = mx + c................1
2x + 6y - 7 = 0
m = -1/3 so the eq of line which is parallel to above line is
y = -x/3 + c ................2
y intercept = (0,c)
x intercept = (3c,0)
y using distance formula , distance bw these two points will be
d = (9c^2 + c^2)1/2 = (+ or - )(root10)c (distance bw coordinate axis)
d = 10 (given) so
c = + or - (root10)
there are two possible values for c so total number of lines can be 2 ...