Question

Given a line X1 66, Y1 69 to X2 -57, Y2 -79 and a point PX 81, PY -49 Find the Signed Cartesian Distance of the point to the line. To receive credit for a question you must show your work! Tip: A Gradient distance is not the same as a Cartesian distance but is related.

Answer 1

the answer is 192.44 to 2 decimal places

Explanation:

For two points P1 = (x1, y1) and P2 = (x2, y2) in the Cartesian plane, the distance between P1 and P2 is defined as

`\sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)\\`

=
`\sqrt{(-57 - 66)^(2) + (-79 - 69)^(2)}`

=
`\sqrt{(-123) ^(2)+ (-148) ^(2)`

=
`\sqrt{15129 + 21904`

=
`\sqrt{37033`

=
`192.44` to 2 decimal places