points A and B are in the first quadrant. point Ois the origin.If the slope of OA is 1, slope of OB is 7 and OA= OB, then slope of AB is -------

Hi Deepu,

Draw the figure.

Let A be angle of OA with x-axis, and B be the angle of OB with x-axis.

Let m be the required slope. Let Q be the (in acute sense) angle made by AB with horizontal.

So m = -tanQ

Now tanA=1, or SinA=1/root2 and cosA=1/root2

and tanB=7, or SinB=7/root50 and cosB=1/root50.

From figure, tanQ = (sinB-sinA)/(cosA-cosB)

or tanQ = (7root2 - root50)/(root50 - root2) = (7-5)/(5-1) = 1/2

or required slope m = -1/2.

Regards,

Ashwin (IIT Madras).