Line ℓ has equation y=x–2. Find the distance between ℓ and the point H(2,5). Round your answer to the nearest tenth

Answer 1

You can do this by finding the equation of the perpendicular line which will give you the co-ordinates of one end of the line you need. Then use the distance formula to get the answer.

Or you can use the formula d =(Ax + By + C)/sqrt(A² + B²)

where Ax + By + C is the equation of the line in standard form and (x,y) is the point in question.

Answer 2

Perpendicular line that eats (2,5)

Slope must be -1

B = y - mx = 5 - (-1)(2) = 5 + 2 = 7

y = -x + 7

They intersect at -x+7 = x-2

7+2 = 2x

9 = 2x

9/2 = x

Intersection (9/2, 5/2)

Distance from (9/2,5/2) to (2,5)

sqrt ( (5/2)^2 + (-5/2)^2 ) = sqrt ( 25/4 + 25/4) = sqrt( 50/4) = 5*sqrt(2)/2