Question

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).

Answer 1

The line is passes through the origin. Another point which lies on the line is the mid-point of the line segment joining the points P( 0,−4 ) and B( 8,0 ).

Let the mid-point of line segment joining the points P( 0,−4 ) and B( 8,0 ) is ( p,q ).

The formula for the mid-point of any line segment passing through point ( x 1 , y 1 ) and ( x 2 , y 2 )is,

( p,q )=( x 1 + x 2 2 , y 1 + y 2 2 )(1)

Substitute the values of ( x 1 , y 1 ) and ( x 2 , y 2 ) as ( 0,−4 ) and ( 8,0 ) in equation (1).

( p,q )=( 0+8 2 , −4+0 2 ) =( 8 2 , −4 2 ) =( 4,−2 )

Now, the formula of slope of a line passing through two different points is given by,

m= y 2 − y 1 x 2 − x 1 (2)

Let, m 1 be the slope of the line passing through points ( 4,−2 ) and ( 0,0 ).

Substitute the values of ( x 1 , y 1 ) and ( x 2 , y 2 ) as ( 0,0 ) and ( 4,−2 ) in equation (2),

m 1 = −2−0 4−0 = −2 4 = −1 2

Thus, the slope of the line passing through the origin and the mid-point of the line segment joining the points P( 0,−4 ) and B( 8,0 ) is − 1 2 .