Determine the distance between the following points and lines

ttpp1124 · Apr 5, 2020

Handwritten solution to a) distance from point p(3, 7) to the line 2x - 5y + 8 = 0: d = |Ax1 + By1 + C| / sqrt(A^2 + B^2) = |2(3) + 5(7) + 8| / sqrt(2^2 + 3^2) = 49/sqrt(13) ≈ 13.59.

LCKurtz · Apr 6, 2020

Have you drawn a graph? 13.6 looks quite a bit too big. I get about 6.8 with a different method.
Edit: See below.

archaic · Apr 6, 2020

Have a look at this graph:

Graph in the xy-plane showing a blue line crossing the y-axis at (0, -1.6), a green point labelled (3, 7), and a purple segment from that point perpendicular to the line, meeting it near x = 5.5.

I have got what LCKurtz have found, exactly ##\frac{37}{\sqrt{29}}##.

LCKurtz · Apr 6, 2020

Your graph is incorrect. The y intercept should be positive and the x intercept negative. And my answer (posting when tired) in post #1 (and yours) is incorrect . The correct answer should be ##\frac {21}{\sqrt{29}}##.

archaic · Apr 6, 2020

LCKurtz said:

Your graph is incorrect. The y intercept should be positive and the x intercept negative. And my answer (posting when tired) in post #1 (and yours) is incorrect . The correct answer should be ##\frac {21}{\sqrt{29}}##.

Ugh, a sign mistake.

Graph on a grid with two straight lines: a green line steeper and falling through the point (3, 7), and a red line rising from the point (0, 1.6).

Determine the distance between the following points and lines

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