Question

Find the shortest distance from the point (3, 3) to the line y = 14x − 2.

A) 3
B) 7
C) 9
D) 10

Answer 1

The shortest distance from the point (3,3) to the line y = 14x - 2 is approximately 9 units.

Step-by-step explanation:

To find the shortest distance from a point to a line, you need to use the formula for the distance between a point and a line. The formula is:

distance = |ax + by + c| / sqrt(a^2 + b^2)

In this case, the line equation is y = 14x - 2, so we have a=14, b=-1, and c=2. The point is (3,3), so we substitute these values into the formula:

distance = |14(3) - 1(3) + 2| / sqrt(14^2 + (-1)^2)

distance = |42 - 3 + 2| / sqrt(196 + 1)

distance = |41| / sqrt(197)

Therefore, the shortest distance from the point (3,3) to the line y = 14x - 2 is approximately 9 units.