Question

Find the distance between Line L and Point P if Line L contains the points

(6, 4) and (3, 2) and Point P is (9, 11).
• 6.4
• 4.2
• 8.9
• 11.3

Answer 1

(b) 4.2

Explanation:

The distance from a point to a line can be found using the formula. To use it, we need the equation of the line in general form.

We notice that the coordinates of the given points have the same y/x = 2/3 ratio. This means they lie on the line y = 2/3x. The equation for that line, written in general form is ...

y = 2/3x

3y = 2x

2x -3y = 0 . . . . . . general form equation for the line through the points.

The formula for the distance from (x, y) to the line ax+by+c=0 is ...

d = |ax +by +c|/√(a²+b²)

The distance from (x, y) to our line is given by the formula ...

d = |2x -3y|/√(2² +(-3)²)

d = |2x -3y|/√13

For point P(9, 11), the distance to the line is ...

d = |2·9 -3·11|/√13 = |18 -33|/√13 = 15/√13 ≈ 4.2