Question

Q1. Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B.

Answer 1

Explanation:

(i) Find the slope of the line l.

m= rise/run

= (y2-y1)/(x2-x1)

= (8-4)/(9-(-2))

= (8-4)/(9+2)

= 4/11

Gradient= 4/11

(ii) Find the coordinates of the midpoint of the points A and B

Midpoint=( (x1+x2)/2 , (y1+y2)/2)

=( (-2+9)/2, (4+8)/2)

=( 7/2, 12/2)

= (3.5, 6)

(iii) Find the distance between points A and B.

Distance= √(〖( x2-x1)〗^2+〖(y2-y1)〗^2 )

= √(〖( 9-(-2))〗^2+〖(8-4)〗^2 )

=√(〖(9+2)〗^2+〖(4)〗^2 )

=√(〖( 11)〗^2+〖(4)〗^2 )

=√(121+16)

=√137

=11.704

Answer 2

Slope =
`-(1)/(6)`

M(x,y) = (1 , 8.5)

D =
`√(37)`

Explanation:

(i) Slope =
`(rise)/(run)`

=> Slope =
`(8-9)/(4+2)`

=> Slope =
`-(1)/(6)`

(ii) Midpoint

M(x,y) =
`((x1+x2)/(2) , (y1+y2)/(2) )`

M(x,y) =
`((-2+4)/(2) , (9+8)/(2) )`

M(x,y) = (1 , 8.5)

(iii) Distance Formula =
`√((x2-x1)^2+(y2-y1)^2)`

D =
`√((4+2)^2+(8-9)^2)`

D =
`√((6)^2+(-1)^2)`

D =
`√(36+1)`

D =
`√(37)`