When line y= x and parabolas 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 length of line segment OB.
From kumon I level math page 193b
To find the length of line segment OB, we first need to determine the coordinates of points O and B.
Point O is at the origin, so O (0,0).
To find point B, we need to solve for the intersection of the parabolas y=x^2 and y=-1/4x^2.
Setting y=x^2 equal to y=-1/4x^2, we have:
x^2 = -1/4x^2
5/4x^2 = 0
x = 0
Therefore, point B is at (0,0).
Now we can calculate the length of line segment OB using the distance formula:
Length OB = √((x2-x1)^2 + (y2-y1)^2)
Length OB = √((0-0)^2 + (0-0)^2)
Length OB = √(0 + 0)
Length OB = √0
Length OB = 0
Therefore, the length of line segment OB is 0.