Find he point on the line y=3x+4 that is closest

Joanna Benson

Joanna Benson

Answered question

2021-12-12

Find he point on the line y=3x+4 that is closest to the origin.

Answer & Explanation

Jimmy Macias

Jimmy Macias

Beginner2021-12-13Added 30 answers

Step 1
Given, the line equation
y=3x+4 ...(1)
Step 2
Compare y=3x+4 with standard equation of line y=mx+c, we get
m=3
From the point on the given line,draw a perpendicular line terminating at the origin. This perpendicular line has a slope=13.
Step 3
Then the equation of perpendicular line is
y=≡13x ...(2)
Step 4
Equating (1) and (2), we get
3x+4=13x
3x=13x4
3x+13x=4
103x=4
10x=12
x=1,2
Step 5
Substitute x=1,2 in y=13x, we get
y=13(1,2)
y=0,4
Step 6
Therefore, the pointon the line y=3x+4 that is closest to the origin is (1,2;0,4).
Laura Worden

Laura Worden

Beginner2021-12-14Added 45 answers

Step 1
The distance between two points is calculated as d=(x2x1)2+(y2y1)2. In our case x1=0 and y1=0, because we want to calculate the distance from a point to the origin. Therefore, d=x2+y2. But, we know that y=3x+4, so we substitute it in the distance equation.
d=x2+(3x+4)2
d=x2+9x2+24x+16
d=10x2+24x+16
To find the extrema, we should solve the equation d(x)=0
d(x)=0
10x+1210x2+24x+16=0
10x+12=0
10x=12
x=1.2
The point (1.2,0.4) is closest to the origin.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?