| Exercise-I |
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| 11. |
Find the coordinates of the points of trisection of the line segment joining M(4 , 5) and N(10 , 11) |
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a) (6 , 7) (8 , 7) |
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b) (6 , 7) (9 , 8) |
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c) (7 , 6) (8 , 9) |
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d) (6 , 7) (8 , 9) |
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| 1. b |
2. c |
3. c |
4. b |
5. d |
| 6. c |
7. d |
8. c |
9. c |
10. c |
| 11. d |
12. b |
13. b |
14. a |
15. c |
| 16. c |
| 1. |
Find the distance between (– 3 , 4) and (7 , – 8) |
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x1 |
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– 3 |
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x2 |
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7 |
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y1 |
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4 |
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y2 |
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– 8 |
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Distance |
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| 2. |
Find the distance between (0 , – 6) and the origin |
| Sol: |
x1 |
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0 |
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x2 |
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6 |
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y1 |
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0 |
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y2 |
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– 6 |
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Distance |
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| 3. |
X is the point on the y axis with 6 as ordinate and B(– 3 , 2) is the other point. Find the length of XB |
| Sol: |
X |
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(0 , 6) |
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B |
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(– 3 , 2) |
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Distance between XB |
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5 |
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| 4. |
If the distance between M(a , 2) is equidistant from A(8 , – 2) , B(2 , – 2) find the value of a |
| Sol: |
put a = 5 then distance between (5 , 2) and (8 , – 2) |
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Distance |
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5units |
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put a = 5 then distance between (5 , 2) and (2 , – 2) is |
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Distance |
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5 units |
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As MA = MB a = 5 |
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| 5. |
What point on the X axis is equidistance from A(5 , 4) and B(– 2 , 3) |
| Sol: |
Distance between (2 , 0) (5 , 4) is |
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Distance |
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5 units |
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Distance between (2 , 0) and (– 2 , 3) is |
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Distance |
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5 units |
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| 6. |
(4 , 0) (0 , 0) (0 , 3) are vertices of an |
| Sol: |
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The vertices represent a right angled triangle |
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| 7. |
(0 , 0) (0 , 8) (8 , 0) represent the vertices of |
| Sol: |
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AB |
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8 units |
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BC |
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8 units |
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90° |
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| 8. |

The quadrilateral PQRS is a |
| Sol: |
In PQRS diagonals PR and QS bisect at right angle. Diagonal QS ≠ PR and the lengths of sides are equal. PQRS is a Rhombus |
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| 9. |
The centre of a circle is (11 , 2). If p(5 , – 6) is a point on its circumference then the length of the radius is |
| Sol: |
x1 = 11 , x2 = 5 , y1 = 2 , y2 = – 6 |
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Radius of the circle |
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10 units |
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| 10. |
Find the coordinates of the point P which divides the line segment joining A(8 , 9) and B(– 7 , 4) internally in the ratio 4 : 3 |
| Sol: |
x1 = 8 , x2 = – 7, y1 = 9 , y2 = – 4 , m : n = 4 : 3 |
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The coordinates at P |
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| 11. |
Find the coordinates of the points of trisection of the line segment joining M(4 , 5) and N(10 , 11) |
| Sol: |
Let P and Q be the points of trisection of the line segment MN |
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P divides MN in the ratio 1 : 2 |
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Q divides MN in the ratio 2 : 1 |
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x1 = 4 , x2 = 10 , y1 = 5 , y2 = 11 , m : n = 1 : 2 |
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coordinates at P are |
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coordinates at Q are |
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x1 = 4 , x2 = 10 , y1 = 5 , y2 = 11 |
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P = (6 , 7) and Q = (8 , 9) are the points of trisection |
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| 12. |
Find the midpoint of the line segment joining the points A(– 5 , 2) and B(– 3 , 6) |
| Sol: |
x1 = – 5, x2 = – 3, y1 = 2 , y2 = 6 |
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Midpoint of AB |
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(– 4 , 4) |
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| 13. |
If midpoint (2a , 6) and (5 , 3b) is (3 , – 4) then the value of a and b are |
| Sol: |
x1 = 2a , x2 = 5 , y1 = 6 , y2 = 3b |
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Midpoint = (3 , – 4) |
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| 14. |
In what ratio x divides the line segment joining (5 , 7) and (6 , – 8) |
| Sol: |
x1 = 5 , x2 = 6 , y1 = 7 , y2 = – 8 |
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Point on X axis (x , 0) |
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Ratio is m : n |
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| 15. |
Find the centroid of the triangle whose vertices are (– 7 , 6) (– 2 , – 5) (4 , 8) |
| Sol: |
x1 = – 7, x2 = – 2, x3 = 4 |
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y1 = 6 , y2 = – 5 , y3 = 8 |
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| 16. |
If A(7 , 4) , B(– 5 , – 5) and C(x , – 2) are the vertices of ΔABC whose centroid is the origin. calculate x , y |
| Sol: |
x1 = 7, x2 = – 5, x3 = x |
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y1 = y , y2 = – 5 , y3 = – 2 |
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centroid = (0 , 0) |
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(x , y ) = ( – 2 , 7) |
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