Answer:
1.34 units.
Explanation:
The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.
Let this line be y = -1/2x + c.
Its passes through (4, 6) so:
6 = -1/2*4 + c
6 = -2 + c
c = 6 + 2 = 8
So, equation of this line is y = -1/2x + 8.
Now we find the point where the 2 lines intersect:
y = 2x - 5
y = -1/2x + 8
2x - 5 = -1/2x + 8
2x + 1/2 x = 5 + 8
(5/2)x = 13
x = 26/5
= 5.2.
and y = 2(5.2) - 5
= 5.4.
So, the point of intersection is (5.2, 5.4)
and the distance between the point (4,6) and the line y = 2x - 5
= √((6 - 5.4)^2 + (4-5.2)^2)
= √(0.36 + 1.44)
= √1.8
= 1.34
There is a formula you can use directly to solve this.