1- the perpendicular bisector of line segment joining the points a(1,5) b(4,6) cuts y axis at which point

2-if the point p (2,1)lies on the line segment joining points a(4,2 ) and b (8,4) then

a- ap=1/3ab , b- ap=pb, c- pb=1/3ab d- ap=1/2 ab choose the correct option

i m getting the relation ab=4 ab am i right or wrong plz specify this

3- show that a (-3,-1), b- (-4,-1), c(3,3) , d (4,3) r the vertices of rhombus i m not getting rhombus

1.

The given point are A(1, 5) and B(4, 6).

Let the line CD be the perpendicular bisector of line segment AB.

Suppose CD intersect AB in E.

∴ Coordinates of E

Let the slope of CD be *m*.

Since AB ⊥ CD,

∴ Slope of CD × Slope of AB = – 1

∴ Equation of CD is

∴ Equation of perpendicular bisector line segment AB is 6*x* + 2*y* – 26 = 0.

We know that, on the *y-*axis, *x* = 0.

Putting *x *= 0 in 6*x* + 2*y* – 26 = 0, we get

0 + 2*y* – 26 = 0

∴ 2*y* = 26

⇒* y *= 13

Thus, the perpendicular bisector of line segment AB cuts *y-*axis at (0, 13).

2.

Given, P(2, 1) lies on the line segment joining A(4, 2) and B(8, 4).

Using distance formula,

3.

The points A( – 3, – 1), B( – 4, – 1), C( 3, 3) and D( 4, 3) are **not** the vertices of the rhombus.

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