Coordinate Geometry – Straight Lines Quiz - ICSE Class 11 Mathematics
Free practice quiz: Coordinate Geometry – Straight Lines (ICSE Class 11 Mathematics). 51 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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The equation of a straight line passing through the origin and inclined at an angle of 135 degrees with the positive x-axis is:
- y = x
- y = -x
- x + y = 0
- y = x + 1
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Answer: B. y = -x
The angle of inclination is 135 degrees. The slope 'm' of a line is given by tan(theta). So, m = tan(135) = tan(180 - 45) = -tan(45) = -1. The equation of a line passing through the origin (0,0) with slope 'm' is y = mx. Therefore, y = -1*x, which simplifies to y = -x.
The lines 3x + 4y - 7 = 0 and 4x - 3y + 5 = 0 are:
- Parallel
- Perpendicular
- Identical
- Intersecting at (1,1)
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Answer: B. Perpendicular
The slope of the first line 3x + 4y - 7 = 0 is m1 = -3/4. The slope of the second line 4x - 3y + 5 = 0 is m2 = -4/-3 = 4/3. The product of their slopes is m1 * m2 = (-3/4) * (4/3) = -1. Since the product of the slopes is -1, the lines are perpendicular.
Find the equation of the line passing through the origin and perpendicular to the line joining the points (2, 3) and (4, 5).
- x + y - 0 = 0
- x - y + 0 = 0
- x + y - 1 = 0
- x - y + 1 = 0
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Answer: A. x + y - 0 = 0
First, find the slope of the line joining (2, 3) and (4, 5). m1 = (5 - 3) / (4 - 2) = 2 / 2 = 1. The slope of a line perpendicular to this line is m2 = -1/m1 = -1/1 = -1. The line passes through the origin (0, 0) and has a slope of -1. Using the point-slope form y - y1 = m(x - x1): y - 0 = -1(x - 0) => y = -x. Rearranging this equation gives x + y = 0.
Find the equation of the line passing through (1, 3) and parallel to the line y = 2x + 5.
- y = 2x + 1
- y = 2x - 1
- 2x - y + 1 = 0
- 2x - y - 1 = 0
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Answer: A. y = 2x + 1
The given line is y = 2x + 5. Its slope is m = 2. A line parallel to this will have the same slope, m = 2. The equation of a line passing through (1, 3) with slope 2 is y - 3 = 2(x - 1) => y - 3 = 2x - 2 => y = 2x + 1.
The equation of the line passing through (0, 0) and (a, b) is:
- bx - ay = 0
- ax - by = 0
- bx + ay = 0
- ax + by = 0
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Answer: A. bx - ay = 0
The slope of the line passing through (0, 0) and (a, b) is m = (b - 0) / (a - 0) = b/a (assuming a != 0). The equation of the line passing through the origin with slope m is y = mx. So, y = (b/a)x. Multiplying by a gives ay = bx. Rearranging this equation gives bx - ay = 0.