Question

Is Point M the midpoint of AB? Select Yes or No for each statement.

Answer 1

A). Yes

B). Yes

C). No

D). Yes

Explanation:

Coordinates of the midpoint of a segment joining two points
`(x_1, y_1)` and
`(x_2,y_2)` are given by
`((x_1+x_2)/(2),(y_1+y_2)/(2))`.

A). If the points are A(1, 2) and B(3, 4)

Coordinates of the midpoint M →
`((1+3)/(2),(2+4)/(2))`

M → (2, 3)

Yes.

B). Extreme points of segment AB are A(0, 8) and B(10, -1)

Coordinates of the midpoint will be,

M →
`((0+10)/(2), (8-1)/(2))`

M → (5, 3.5)

Yes

C). Extreme points of segment AB are A(-7, -5) and B(6, 4)

Coordinates of the midpoint will be,

M →
`((-7+6)/(2), (-5+4)/(2))`

M → (-0.5, -0.5)

NO

D). Extreme points of segment AB are A(4, -2) and B(6, -8)

Coordinates of the midpoint will be,

M →
`((4+6)/(2), (-2-8)/(2))`

M → (5, -5)

Yes