A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the point on the line y = 4x+2 that is closest to the origin.
Solution:
The point on the line y = 4x + 2 which is closest to the origin will be on the line perpendicular to the origin.
y = 4x + 2 [Given]
Slope m1 = 4
We know that when two lines are perpendicular to each other
m1 . m2 = -1
So we get
m2 = -1 / m1
m2 = -1/4
y = -1/4 x
Let us substitute the value of y in the equation given
-1/4 x = 4x + 2
-1/4 x - 4x = 2
By taking LCM
(-1 - 16)/4 x = 2
-17/4 x = 2
Now by cross multiplying
x = 2 x -4/17
x = -8/17
Substitute the value of x
y = -1/4 (-8/17) = 2/17
Therefore, the point closest to the origin is (-8/17, 2/17).
Find the point on the line y = 4x+2 that is closest to the origin.
Summary:
The point on the line y = 4x+2 that is closest to the origin is (-8/17, 2/17).
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