Find the distance from the point (0,0) to the line y = x – 6. Round your answer to the nearest tenth.

Question

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Answer 1

y=x-6 to the origin (0,0)

the equation is a line with slope = 1, and y intercept -6

find the equation of the perpendicular line through the origin.

then find where they intersect. find that point and calculate the distance

from it to the origin

a perpendicular line has a negative inverse slope.

which is -1/1 =-1

y=-x+b find b by plugging in the point (0,0)

0=0+b

b=0

y=-x intersects y=x-6 when

-x =x -6 or

2x =6

x =3, the point (3,-3)

now find the distance from (3,-3) to (0,0) which

is d^2 =3^2 +3^2 = 18

d= sqr18 = 3sqr2 = about 3(1.414) = 4.2

graph the lines, you'll see a right triangle formed

with sides 3, 3 and 3sqr2, where 3sqr2 = hypotenuse = distance from the line to the origin