What is the distance of the line x+6y-7=0 from the origin?
Please help, is my answer -7sqrt37/37 correct? If not, please help me whats the right solution
If (a,b) is any point, its distance to the line
Ax + By + C = 0 is
|Aa + Bb + C|/(A^2 + B^2)
so your point is (0,0)
distance
= |0+0-7|/(1+36)
= 7/√37
which the probably rationalized .
7/√37 * √37/√37 = 7√37/37
To find the distance from the origin to a line, you can use the formula:
Distance = |Ax + By + C| / √(A^2 + B^2)
In this case, the equation of the line is x + 6y - 7 = 0. Comparing it to the general form Ax + By + C = 0, we have A = 1, B = 6, and C = -7.
Now, substitute these values into the formula:
Distance = |1(0) + 6(0) - 7| / √(1^2 + 6^2)
= |-7| / √(1 + 36)
= 7 / √37
Simplifying further by rationalizing the denominator:
Distance = 7 / √37 * (√37 / √37)
= 7√37 / 37
Thus, the correct answer is 7√37 / 37.