The mid point of 2 co-ordinates x - y and a - b isA- x-a - 2-y-b - 2B- x-b-y-aC- x-b - 2-y-b - 2D- x-a- y-b

The correct option is A ((x+a)/2 , (y+b)/2) Mid point of 2 co ordinates (x,y) and (a,b) is given by (x + a)/2 , (y + b)/2. Mid point formula is a sp ...

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Standard X

Mathematics

Triplicate Ratio

The mid point...

Question

The mid point of 2 co-ordinates (x,y) and (a,b) is

(x+a , y+b)

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((x+a)/2 , (y+b)/2)

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((x+b) , (y+a))

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((x+b)/2 , (y+b)/2)

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Solution

The correct option is B
((x+a)/2 , (y+b)/2)

Mid point of 2 co-ordinates (x,y) and (a,b) is given by $\frac{(x + a)}{2}$ , $\frac{(y + b)}{2}$ .

Mid point formula is a special case of section formula where the ratio of division is 1:1.

The section formula dividing 2 co-ordinates (x₁ , y₁) and (x₂ , y₂) in ratio m:n is

$[\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}]$

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Similar questions

Q. If a variable straight line is drawn through the point of intersection of

\frac{x}{a} + \frac{y}{b} = 1

and

\frac{x}{b} + \frac{y}{a} = 1

meets the co-ordinate axes at

A

and

B

, then the locus of the mid-point of line segment

A B

Q. If

y = \frac{2}{\sqrt{a^{2} - b^{2}}} \tan^{- 1} (\frac{a - b}{a + b} \tan \frac{x}{2}), a > b > 0

, then

(a)

y_{1} = \frac{- 1}{a + b \cos x}

(b)

y_{2} = \frac{b \sin x}{{(a + b \cos x)}^{2}}

(c)

y_{1} = \frac{1}{a - b \cos x}

(d)

y_{2} = \frac{- b \sin x}{{(a - b \cos x)}^{2}}

The locus of the mid points of the chords of the circle $x^{2} + y^{2} - a x - b y = 0$ which subtend a right angle at $(\frac{a}{2}, \frac{b}{2})$ is :

The locus of the point of intersection of perpendicular tangents to the circles $x^{2} + y^{2} = a^{2} a n d x^{2} + y^{2} = b^{2} i s$

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