Help me please .........////// 10 points \\\\\\\

Find the foot of the perpendicular from the point (2,4) to the line x + y = 1

x + y = 1 has slope -1

so the perpendicular has slope 1

let the point (x1,y1) be the point of intersection between the line x + y = 1 and the perpendicular .

so

x1 + y1 = 1 => y1 = 1 - x1 ---- (1)

and y1 - 4 / x1 - 2 = 1

=> y1 - 4 = x1 - 2

from (1) : 1 - x1 - 4 = x1 - 2

=> 2x1 = -1 => x1 = - 0.5

so y1 = 1- (-0.5) = 1.5

so the point is (-0.5 , 1.5)

the perpendicular drawn to line x + y = 1 will have slope 1 by m1m2 = -1

let the point that intersects x + y =1 be (x1 , y1)

eqn of the perpendicular :- y - 4 = 1( x-2 )

=> y = x + 2

now ( x1 , y1) will satisfy both y = x+2 and x + y = 1

so y1 = x1 + 2 and x1 + y1 = 1

solve both and you'll get x1 = -1/2 and y1 = 3/2

(-0.5 , 1.5)