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By using the formula y-y1 = m(x-x1) form an equation from (2, 4) with a slope of -1/2x which is the negative reciprocal of 2x:-

y-4 = -1/2(x-2)

y = -1/2x+5 => 2y = -x+10

Then find the point of intersection of 2y = -x+10 and y = 2x+10 which works out as (-2, 6)

The perpendicular distance from (2, 4) to (-2, 6) is:-

(x1-x2)2 + (y1-y2)2 = distance2

(2-(-2))2 + (4-6)2 = 20 and the square root of this is the distance between the points.

Therefore the distance is the square root of 20 which works out as 2 times the square root of 5.

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Q: How do you work out the perpendicular distance from the point 2 4 to the straight line of y equals 2x plus 10?
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