The Point O Is(0,0) and Point B is(6,9).Point A lies on the line OB.The ratio of OA:AB=2:1.Find the coordinates of Point A. (Method Needed Mostly)thanks....
A is 2/3 of the way from O to B.
So, the x- and y-values are 2/3 of the way from (0,0) to (6,9).
That help some?
Why Is A 2/3 of OB and not 1/3 Steve?
because OA:AB = 2:1
Draw the line OB of length 3
Mark point A such that
OA=2
AB=1
A is 2/3 of the way from O to B
Ok Steve I will Try It .But How Steve? And What If I Used 1/3 In regards from B to 0.A is 1/3 of The way from B to O.Will the answer remain the same.
Yes, you can say A is 1/3 of the way from B to O
That's the same as saying A is 2/3 of the way from O to B.
To find the coordinates of Point A on the line OB, we can use the concept of ratio and the distance formula.
Given:
Point O is (0,0).
Point B is (6,9).
The ratio of OA:AB is 2:1.
Let's calculate the coordinates of Point A step by step:
Step 1: Calculate the distance between Points O and B.
We can use the distance formula to find the length of OB:
OB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
OB = sqrt((6 - 0)^2 + (9 - 0)^2)
OB = sqrt(36 + 81)
OB = sqrt(117)
Step 2: Divide the distance OB in the ratio of 2:1.
Since the ratio of OA:AB is 2:1, we need to divide the distance OB into three parts, with two parts for OA and one part for AB.
Let's assume:
OA = 2x
AB = x
Step 3: Calculate the coordinates of Point A.
To find the coordinates of Point A, we need to calculate the x-coordinate and the y-coordinate separately.
x-coordinate of A:
The x-coordinate of Point A can be calculated using the following equation:
x-coordinate of A = x-coordinate of O + 2x-coordinate of OA
x-coordinate of A = 0 + 2 * (6 - 0) / 3
x-coordinate of A = 2 * 6 / 3
x-coordinate of A = 4
y-coordinate of A:
The y-coordinate of Point A can be calculated using the following equation:
y-coordinate of A = y-coordinate of O + 2y-coordinate of OA
y-coordinate of A = 0 + 2 * (9 - 0) / 3
y-coordinate of A = 2 * 9 / 3
y-coordinate of A = 6
Therefore, Point A has coordinates (4, 6).