MATH SOLVE

6 months ago

Q:
# Find the point on the line y = 5x + 4 that is closest to the origin. (x, y) = $$− 10 13, 2 13

Accepted Solution

A:

we know that

the point on the line y = 5x + 4 that is closest to the origin will be on the perpendicular line through the origin,

the line

y=5x+4---------> the slope is m1=5

if two lines are perpendicular

m1*m2=-1-----------> m2=-1/m1

so

m2=-1/5

y = (-1/5)x

so will satisfy

(-1/5)x = 5x +4

(-26/5)x = 4

x = 4*(-5/26) = -10/13

y = (-1/5)x = 2/13

The answer is

the point (-10/13, 2/13)

see the attached figure

the point on the line y = 5x + 4 that is closest to the origin will be on the perpendicular line through the origin,

the line

y=5x+4---------> the slope is m1=5

if two lines are perpendicular

m1*m2=-1-----------> m2=-1/m1

so

m2=-1/5

y = (-1/5)x

so will satisfy

(-1/5)x = 5x +4

(-26/5)x = 4

x = 4*(-5/26) = -10/13

y = (-1/5)x = 2/13

The answer is

the point (-10/13, 2/13)

see the attached figure