Answer:
3.33
Explanation:
1st get the line in point slope form (y = mx + b)
-2X + 3y + 3 = 0
3y = 2x - 3
y = (2/3)x - (3/3)
y = (2/3)x - 1 (slope = 2/3 and y-intercept is -1)
The distance from a point to a line is line segment starting at the point and perpendicular (shortest distance) to 1st line. A line perpendicular to the 1st line will have a negative inverse slope. So the line created in point slope form will look like
y = mx + b
y = (-3/2)x + b and using the given point (3,5)
5 = (-3/2)3 + b
5 - (-3/2)3 = b
5 + 9/2 = b
b = 19/2 So it's equation is
y = (-3/2)x + 19/2
At the point where the segment intersects the 1st line, that point must solve both equations, so we can set the equation equal to each other (both y's and both x's same).
(2/3)x -1 = (-3/2)x + 19/2
(2/3)x - (-3/2)x = 1 + 19/2
(2/3 + 3/2)x = 21/2
x = (21/2) / (2/3 + 3/2) = 4.846, now plug that into the 1st equation to get y
y = (2/3)x - 1
y = (2/3)4.846 - 1
y = 2.231 so the intersection point is (4.846,2.231) from (3,5).
Because of the pythagorean theorem (the two points form a right triangle) the distance will be
C**2 = A**2 + B**2
= (4.846 - 3)**2 + (2.231 - 5)**2
= 1.846**2 + (2.769)**2
C = 3.33