When line y= x and parabola y= x squared and y= -1/4x squared intersect at points A and B in addition to at origin O as shown below, find the lengths of line segments OA and OB.
from Kumon level I math page 191b
To find the lengths of line segments OA and OB, we first need to find the coordinates of points A and B.
Equating the equations of the parabola and the line, we get:
x^2 = x
x^2 - x = 0
x(x - 1) = 0
So, x = 0 or x = 1
When x = 0, y = 0 (origin O)
When x = 1, y = 1 (point A)
When x = 1, y = 1 (point B)
Now, we can find the lengths of line segments OA and OB using the distance formula:
OA = √((1-0)^2 + (1-0)^2) = √2
OB = √((1-0)^2 + (1-0)^2) = √2
Therefore, the lengths of line segments OA and OB are both √2.