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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
What is the point on the line y = 2x + 3 that is closest to the origin?
Solution:
The point on line y = 2x + 3 closest to the origin is the point of intersection of y = 2x +3 and line perpendicular to it passing through (0, 0).
We know that equation of line perpendicular to Ax + By + C = 0 and passing through (x1, y1) is
B(x - x1) - A(y - y1) = 0.
Here, A = 2, B = -1 and (x1, y1) = (0, 0)
⇒ -1(x - 0) -2(y - 0) = 0
⇒ x + 2y = 0 --- (1)
Now, the nearest point on line y = 2x + 3 from the origin is the point of intersection of 2x - y + 3 = 0 and x + 2y = 0.
Solving, x + 3(3x + 4) = 0
⇒ 10x + 12 = 0
⇒ x = -12/10
⇒ x = -6/5
Substitute the x = -6/5 in equation(1)
⇒ -6/5 + 2y = 0
⇒ y = 3/5
Therefore, the required point is (-6/5, 3/5)
What is the point on the line y = 2x + 3 that is closest to the origin?
Summary:
The point on the line y = 2x + 3 that is closest to the origin is (-6/5, 3/5).
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