6 COORDINATE GEOMETRY - 6. COORDINATE GEOMETRY Unit 6.1 :...

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6. Coordinate Geometry 1 6. COORDINATE GEOMETRY Unit 6.1 : To Find the distance between two points [BACK TO BASICS] A( 1 1 , y x ) and B( 2 2 , y x ) : AB = 2 2 2 1 2 1 ( ) ( ) x x y y - + - . Eg. 1 Given two points A(2,3) and B(4,7) Distance of AB = 2 2 (4 2) (7 3) - + - = 4 16 + = 20 unit. E1. P(4,5) and Q(3,2) PQ = [ 10 ] E2. R(5,0) and S(5,2) [2] E3. T(7,1) and U(2,5) [ 41 ] E4. V(10,6) and W(4,2) [ 52 ] E5. X(-4,-1) and Y(-2,1) [ 18 ] More challenging Questions…. E1. The distance between two points A(1, 3) and B(4, k) is 5. Find the possible vales of k. 7, -1 E2. The distance between two points P(-1, 3) and Q(k, 9) is 10. Find the possible values of k. 7, -9 E3. The distance between two points R(-2, 5) and S(1, k) is 10 . Find the possible vales of k. 6, 4 E4. The distance between two points K(-1, p) and L(p, 9) is 50 . Find p. p = 0, 6 E5. The distance between two points U(4, -5) and V(2, t) is 20 . Find the possible vales of t. t =-9, -1 E6. If the distance between O(0, 0) and P(k, 2k) is the same as the distance between the points A(-4, 3) and B(1, -7), find the possible values of k. k = 5, -5
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6. Coordinate Geometry 2 Unit 6.2 : Division of a Line Segment 6.2.1 To find the mid-point of Two Given Points. Formula : Midpoint M = + + 2 , 2 2 1 2 1 y y x x Eg. P(3, 2) and Q(5, 7) Midpoint, M = + + 2 7 2 , 2 5 3 = (4 , 2 9 ) E1 P(-4, 6) and Q(8, 0) (2, 3) E2 P(6, 3) and Q(2, -1) (4, 1) E3 P(0,-1), and Q(-1, -5) (- ½ , -3) 6.2.2 Division of a Line Segment Q divides the line segment PR in the ratio PQ : QR = m : n. P( x , y ), R( x , y ) Q (x,y) = + + + + n m my ny n m mx nx 2 1 2 1 , (NOTE : Students are strongly advised to sketch a line segment before applying the formula) Eg1. The point P internally divides the line segment joining the point M(3,7) and N(6,2) in the ratio 2 : 1. Find the coordinates of point P. P = + + + + 1 2 ) 2 ( 2 ) 7 ( 1 , 1 2 ) 6 ( 2 ) 3 ( 1 = 3 11 , 3 15 = 11 5, 3 E1. The point P internally divides the line segment joining the point M (4,5) and N(-8,-5) in the ratio 1 : 3. Find the coordinates of point P. 5 1, 2 n m P(x 1 , y 1 ) R(x 2 , y 2 ) Q(x, y) n m R(x 2 , y 2 ) P(x 1 , y 1 ) Q(x, y) 1 2 N(6, 2) M(3, 7) P(x, y)
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6. Coordinate Geometry 3 More Exercise : The Ratio Theorem (NOTE : Students are strongly advised to sketch a line segment before applying the formula) E1. R divides PQ in the ratio 2 : 1. Find the coordinates of R if (a) P(1, 2) and Q( -5, 11) (b) P(-4, 7) and Q(8, -5) (a) (-3, 8) (b) (4 , -1) E2. P divides AB in the ratio 3 : 2. Find the coordinates of P if (c) A(2, -3) and B( -8, 7) (d) A(-7, 5) and B(8, -5) (a) (-4, -3) (b) (2 , -1) E3. M is a point that lies on the straight line RS such that 3RM = MS. If the coordinates of the points R and S are (4,5) and (-8,-5) respectively, find the coordinates of point M. 3RM = MS
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6 COORDINATE GEOMETRY - 6. COORDINATE GEOMETRY Unit 6.1 :...

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