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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