Question

Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).

Answer 1

2.5√2 units

Explanation:

The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.

~~~~~~~~~~~~~~~~~~~~~

y = - x + 5 , slope m = - 1

Slope of perpendicular line is opposite reciprocal. In our case is 1 .

G ( 6 , 4 )

y - 4 = 1 × ( x - 6 )

y = x - 2

x - 2 = - x + 5 , x = 3.5

y = 1.5

Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )

OG =
`√((6-3.5)^2 +(4-1.5)^2 )` = 2.5√2 units