Question

The coordinates of the foot of the perpendicular drawn from the point (2,3) to the straight line x+y = 11 are ---------

Answer 1

Answer:

(5,6)

Step-by-step explanation:

Given data, Point (2,3) is perpendicular to equation X+Y=11

Rewriting the equation in line equation format ( Y = mX + C)

Y = -X + 11___________________(a)

This shows slope M1 is -1

As the point is perpendicular to this line, M1 x M2 = -1

(-1) x M2 = -1

M2 = 1

Standard equation form, Y = X + C

Substituting the given points (2,3) in above equation.

3 = 2 + C

C = 1

I.e Y = X + 1__________________(b)

Now the coordinate should satisfy both equation (a) & (b)

Thus solving both equations, we can get X = 5, Y= 6

I.e Coordinates (5,6)

Answer 2

Answer:

(5,6)

Step-by-step explanation:

Given data, Point (2,3) is perpendicular to equation X+Y=11

Rewriting the equation in line equation format ( Y = mX + C)

Y = -X + 11___________________(a)

This shows slope M1 is -1

As the point is perpendicular to this line, M1 x M2 = -1

(-1) x M2 = -1

M2 = 1

Standard equation form, Y = X + C

Substituting the given points (2,3) in above equation.

3 = 2 + C

C = 1

I.e Y = X + 1__________________(b)

Now the coordinate should satisfy both equation (a) & (b)

Thus solving both equations, we can get X = 5, Y= 6

I.e Coordinates (5,6)