Explanation:
you have both points : (1, 1) and (5, 5).
so, we don't need to do any triangle calculations to get the height of the main triangle.
all we need to do is calculate the distance between these 2 points.
2 points in a coordinate grid create a right-angled triangle.
the direct distance is the Hypotenuse (the side opposite of the 90° angle). and the legs are the x- and the y-coordinate differences (one up or down the other left or right).
and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse a and b being the legs.
so, how long are these legs here ?
the x-difference is 5 - 1 = 4.
also the y-difference is 5 - 1 = 4
so,
distance² = 4² + 4² = 16 + 16 = 32
distance = sqrt(32) = sqrt(16×2) = 4×sqrt(2) =
= 5.656854249...
the distance of P to the line RQ is 5.656854249...