The shortest distance from a point to a line is the length of the segment perpendicular to the given line.
3sqrt(2)/2≈ 2.1 units
Practice makes perfect
The shortest distance from a point to a line is the length of the segment perpendicular to the given line. We will need to find the perpendicular line, and then we can find the intersection point. Finally, we can calculate the distance from the given point to the point of intersection.
Finding the Perpendicular Line
Perpendicular lines have opposite reciprocal slopes. This means the product of their slopes is equal to -1.
m_1 * m_2=- 1
The given line has a slope of -1.
y=- x+4 ⇔ y= -1x+4By substituting this value into the equation above for m_1, we can find the slope of the perpendicular line.
We can add this value of b, along with the known slope, into the slope-intercept form to have a complete equation for the perpendicular line.
y= 1x+( -3) ⇔ y=x-3
Finding the Point of Intersection
To find the distance, we also need to know where the given line and the perpendicular line intersect. By setting up a system of equations, we can find the point of intersection.
y=- x+4 y=x-3
Since both equations have y isolated, it is most convenient to use the Substitution Method.
Now that we know the two endpoints of the segment, we can use the Distance Formula to calculate the length of the segment from the intersection to the given point.
