WBBSE Class 9 Maths Coordinate Geometry Chapter 2 Internal And External Division Of Straight Line Segment Multiple Choice Questions

WBBSE Class 9 Maths  Coordinate Geometry Chapter 2 Internal And External Division Of Straight Line Segment Multiple Choice Questions

Example 1. The midpoint of line segment joining two points (l, 2m), (-l + 2m, 2l – 2m) is

1. (l, m)
2. (2,- m)
3. (m, -l)
4. (m, l)

Solution: \(\left(\frac{l-l+2 m}{2}, \frac{2 m+2 l-2 m}{2}\right)\) = (m, l)

Example 2. The abscissa at the point P which divides the line segment joining two points A (1, 5), and B (-4, 7) internally in the ratio 2: 3 is

1. 1
2. 11
3. 1
4. -11

Solution: \(\left(\frac{2 \times(-4)+3 \times 1}{2+3}\right)=\frac{-8+3}{5}=-1\)

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Example 3. The coordinates of the end points of a diameter of a circle are (7, 9) and (-1,-3). The coordinates of the centre is

1. (3, 3)
2. (4, 6)
3. (3, -3)
4. (4, -6)

Solution: Centre = \(\left(\frac{7-1}{2}, \frac{9-3}{2}\right)\) = (3, 3)

Example 4. A point which divides the line segment joining two points (2, -5), (-3, -2) externally in 4: 3 The coordinates of point is

1. -18
2. -7
3. 18
4. 7

Solution: Co-ordinates = \(\left(\frac{-3 \times 4-3 \times 2}{4-3}, \frac{4(-2)-3(-5)}{4-3}\right)\) = (-18, 7)

Example 5. If the points P (1, 2), Q (4, 6), R (5, 7), and S (X, Y) are the vertices of a parallelogram PQRS then

1. x = 2, y = 4
2. x = 3, y = 4
3. x = 2, y = 3
4. x = 2, y = 5

Solution: Midpoint of PR = \(\left(\frac{5+1}{2}, \frac{7+2}{2}\right)=\left(3, \frac{9}{2}\right)\)

Midpoint of QS = \(=\left(\frac{4+x}{2}, \frac{6+y}{2}\right)\)

∴ \(\frac{4+y}{2}=3 \Rightarrow x=2, \quad \frac{9}{2}=\frac{6+y}{2}, \quad y=3\)

Example 6. The coordinates of the midpoint of the line segment joining the points (a + b, a- b) and (a – b, a + b) is

1. (a, b)
2. (a, a)
3. (b, b)
4. (2a, 2b)

Solution: \(\left(\frac{a+b+a-b}{2}, \frac{a-b+a+b}{2}\right)=(a, a)\)

Example 7. The coordinates of the midpoint of the line segment joining the points (1 – a, -2a), (2a – 2, a + 1) are

1. \(\left(\frac{a-1}{2}, \frac{1-a}{2}\right)\)
2. \(\left(\frac{2 a-1}{2}, \frac{1-2 a}{2}\right)\)
3. \(\left(\frac{a+3}{2}, \frac{-3 a+1}{2}\right)\)
4. \(\left(\frac{a+1}{2}, \frac{2 a+1}{2}\right)\)

Solution: \(\left(\frac{1-a+2 a-2}{2}, \frac{-2 a+a+1}{2}\right)=\left(\frac{a-1}{2}, \frac{1-a}{2}\right)\)

Example 8. The coordinates of the midpoint P of the line segment joining the points A (-m, 6), and B (4, n) are (-1, -1). The value of m and n are

1. 6, 8
2. -6, -8
3. 6, -8,
4. -6, 8

Solution: \(\frac{-m+4}{2}=-1, m=4+2=6, \quad \frac{6+n}{2}=-1, n=-8\)