Question

Find the distance from point A to the given line.

A(3,4) y=-x

Answer 1

The distance from the point (3,4) to the line y = -x is
`(7√(2) )/( 2)` or approximately 4.95 units.

The formula for the distance between a point (x₀,y₀) and a line Ax + By + C = 0 is expressed as:

distance =
`(| Ax_o + By_o + C |)/(√(A^2 + B^2) )`

Given the parameter:

The equation of the line is: y = -x

x + y = 0

Hence, A = 1, B = 1 and C = 0.

Point: (3,4):

x₀ = 3 and y₀ = 4

Plug these values into the above formula and simplify:

distance =
`(| Ax_o + By_o + C |)/(√(A^2 + B^2) )`

`= (| 1(3) + 1(4) + 0 |)/(√(1^2 + 1^2) )\\\\= (| 3 + 4 + 0 |)/(√(1 + 1) )\\\\= (| 7 |)/(√(2) )\\\\= (7)/(√(2) )\\\\= (7√(2) )/( 2) \ or \ 4.95`

Therefore, the distance measures approximately 4.95 units.