# In the picture, the question asked for coordinate of B My teacher guided me by telling that i have to find the length of OA and OB first in case to find B i have no problem to find length of OA...

In the picture, the question asked for coordinate of B

My teacher guided me by telling that i have to find the length of OA and OB first in case to find B

i have no problem to find length of OA but i really struggling on finding OB

It would be great if anyone could help me on finding B and the length of OB :))

Thankyou!

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### 1 Answer

**Given Info**: Triangle ABC, area = 15 square units, OB `_|_` AC, coordinates of A : (6,-3); equation of OB: y =2x; O is origin

**To find**: coordinates of B.

Your teacher is right (of course), you will need to find the lengths of OA and OB first.

To solve the question, we will use the following:

Distance between two points (x1,y1) and (x2,y2) = `sqrt((x2-x1)^2 + (y2-y1)^2)`

area of triangle = 1/2 x height x base

Length OA = `sqrt((6-0)^2 + (-3-0)^2) = sqrt (6^2 + 3^2) = sqrt (45) = 3sqrt5`

And Area of triangle = 1/2 x OA x OB = 15

i.e., OB = 15x2/OA = 15x2/(3`sqrt5` )= 2`sqrt5`

Also, OB = `sqrt((x-0)^2 + (y-0)^2) = sqrt(x^2 + y^2) = 2 sqrt 5`

On simplification, we get `x^2 + y^2 = 20`

using the equation of OB: y = 2x

which means `x^2 + (2x)^2 = x^2 + 4x^2 = 5x^2 = 20`

or, x =2 and y = 2x= 4

Therefore the coordinates of B are **(2,4)**.