MathCity.org Exercise 4.1 (Solutions)



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Exercise 4.1 (Solutions) Page 185

Calculus and Analytic Geometry, MATHEMATICS 12 Available online @ , Version: 3.0

Distance Formula

Let A(x1, y1) and B(x2, y2 ) be two points in a plane and d be a distance between A and B then

d = (x2 - x1)2 + ( y2 - y1)2

A( x1 , y1)

B( x2 , y2)

or d = (x1 - x2 )2 + ( y1 - y2 )2

See proof on book at page181

O(0,0)

Ratio Formula

Let A(x1, y1) and B(x2, y2 ) be two points in a plane. The coordinates of the point C dividing the line segment AB in the ratio

k1 : k2 are

k1x2

+

k2 x1

,

k1 y2

+

k2

y1

k1 + k2

k1 + k2

See proof on book at page 182

If C be the midpoint of AB i.e. k1 : k2 = 1:1

then coordinate of C becomes

x1

+ 2

x2

,

y1

+ 2

y2

k1 A( x1 , y1)

k2

C

B( x2 , y2)

O(0,0)

Question # 1

Describe the location in the plane of the point P( x, y) for which

(i) x > 0

(ii) x > 0 and y > 0

(iii) x = 0

(iv) y = 0

(v) x < 0 and y 0

(vi) x = y

(vii) x = - y

(viii) x 3

(ix) x > 2 and y = 2

(x) x and y have opposite signs. Solution (i) x > 0

Right half plane

y 2nd Quadrant 1st Quadrant

(ii) x > 0 and y > 0 The 1st quadrant.

x0

x>0 y>0

(iii) x = 0 y-axis

(iv) y = 0 x-axis

- x

x ................
................

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