Question

5. Find the slope of the line which passes through the origin and the midpoint of
the line segment joining the points ^ h 0 4 ,- and (8 , 0).

Answer 1

Let P ≡ (x, y) is the midpoint of (0, -4) and (8, 0)
use section formula of midpoint ,
e.g., x = (x1 + x2)/2 and y = (y1 + y2)/2
Now, x = (0 + 8)/2 = 4 and y = (-4+0)/2 = -2
Hence, P ≡ (4 , -2)

Now, slope of P ≡ (4,-2) and origin (0,0)
Use formula, if two points (x1,y1) and(x2 ,y2) are given ,
Then, slope = (y2 - y1)/(x2 - x1)
Now, slope = (0 +2)/(0 - 4) = -1/2

Answer 2

Solution :

I ) mid point of line joining

the points

A(0,4) = ( x1 , y1 )

and B(8,0) = ( x2 , y2 )

Coordinates of the midpoint

= [ (x1+x2)/2 , (y1+y2)/2 ]

= [ (0 + 8 )/2 , ( 4 + 0 )/2 ]

= ( 4 , 2 )

According to the problem given ,

Slope of line which passes

through the origin and midpoint

( 4 , 2 ) is

m = y/x

m = 2/4

m = 1/2

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