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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.

2 Answers

3 votes

Answer:

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

User Manoj Acharya
by
7.1k points
4 votes

Answer:

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)

User Max Prokopov
by
7.3k points