Question

Find the distance from point A(−1/4, 5) to the line −x+2y = 14. Round your answer to the nearest tenth.

Answer 1

Explanation:

1.5

Answer 2

Given:

Point is
`A\left(-(1)/(4),5\right)`.

Line is
`-x+2y=14`.

To find:

Distance from point A to given line.

Solution:

The distance of point
`(x_0,y_0)` from line
`ax+by+c=0` is

`d=(|ax_0+by_0+c|)/(√(a^2+b^2))`

Using the above formula, the distance from
`A\left(-(1)/(4),5\right)` to the line
`-x+2y-14=0` is

`d=(|-(-(1)/(4))+2(5)-14|)/(√((-1)^2+(2)^2))`

`d=(0.25+10-14|)/(√(1+4))`

`d=(|-3.75|)/(√(5))`

`d=(3.75)/(√(5))`

`d=1.677`

`d\approx 1.7`

Therefore, the required distance is 1.7 units.