Find the distance between point A(7, -2) and the line y = x + 5. Round your answer to the nearest tenth.

Answer 1

Hello, Teagan,

I'm assuming you are looking for the shortest distance between the line and the point. If we put both on a graph, we can visualize the question and then more easily pick an approach for solving it.

Graph the line y = x + 5 and add point A (7,-2). Then drew a perpendicular line to the y=x+5 that goes through point A.

Unfortunately, there isn't room here for my graph. But once you've done your own, you'll see that we have a right triangle with two sides equal to 7 each. Use the Pythagorean theorem to solve for the distance between point A and the green line, the hypotenuse (H). I get 7*2^(1/2) or close to 9.90.

I hope this helps,

Bob

Answer 2

You need to find the perpendicular distance

y = x + 5 has slope 1

So a line perpendicular to it has slope -1

Such a line going through (7, -2) has equation y- (-2) = -1 (x-7)

y+2 = -x + 7

y = -x + 5

Now find the point of intersection between the two lines

y = x + 5

y = -x + 5

x + 5 = -x + 5

2x = 0

x = 0

y = 5

Now find the distance from A to this point

√ [(7-0)^2 + (5-(-2))^2 ]

This is the required distance