Q.1 Find the distance between the points A(3, 4) and B(7, 1).
5
4
6
3
Explanation - Distance formula: √[(x2-x1)^2 + (y2-y1)^2] = √[(7-3)^2 + (1-4)^2] = √[16+9] = √25 = 5
Correct answer is: 6
Q.2 Find the midpoint of the line segment joining points P(2, -3) and Q(4, 5).
(3, 1)
(1, -1)
(2, 2)
(3, -1)
Explanation - Midpoint formula: ((x1+x2)/2, (y1+y2)/2) = ((2+4)/2, (-3+5)/2) = (3,1)
Correct answer is: (3, 1)
Q.3 Find the slope of the line passing through points (1, 2) and (3, 6).
1
2
3
4
Explanation - Slope formula: m = (y2-y1)/(x2-x1) = (6-2)/(3-1) = 4/2 = 2
Correct answer is: 2
Q.4 The equation of a line parallel to y = 2x + 3 and passing through (1, 4) is:
y = 2x + 2
y = 2x + 3
y = 2x + 2
y = 2x + 2
Explanation - Parallel lines have the same slope. Slope = 2, use point-slope formula: y-4 = 2(x-1) => y = 2x + 2
Correct answer is: y = 2x + 2
Q.5 The equation of a line perpendicular to y = -3x + 5 and passing through the origin is:
y = 3x
y = -1/3x
y = 1/3x
y = -3x
Explanation - Perpendicular slope = negative reciprocal of -3 => 1/3. Passes through origin, so equation: y = (1/3)x
Correct answer is: y = 1/3x
Q.6 The area of a triangle with vertices A(0, 0), B(4, 0), and C(0, 3) is:
6
12
7
5
Explanation - Area = 1/2 * base * height = 1/2 * 4 * 3 = 6
Correct answer is: 6
Q.7 If a line passes through points (2, 3) and (4, k) and has slope 5, then k = ?
8
7
5
6
Explanation - Slope formula: 5 = (k-3)/(4-2) => 5 = (k-3)/2 => k-3 = 10 => k = 13
Correct answer is: 7
Q.8 Find the distance from point (3, -4) to the x-axis.
3
4
5
7
Explanation - Distance from point to x-axis = absolute value of y-coordinate = | -4 | = 4
Correct answer is: 4
Q.9 Find the distance from point (3, -4) to the y-axis.
3
4
5
7
Explanation - Distance from point to y-axis = absolute value of x-coordinate = | 3 | = 3
Correct answer is: 3
Q.10 The coordinates of the centroid of a triangle with vertices A(0, 0), B(6, 0), and C(0, 8) are:
(2, 2)
(2, 8)
(2, 8/3)
(2, 8/3)
Explanation - Centroid formula: ((x1+x2+x3)/3, (y1+y2+y3)/3) = ((0+6+0)/3, (0+0+8)/3) = (2, 8/3)
Correct answer is: (2, 8/3)
Q.11 The equation of a circle with center at (2, -3) and radius 5 is:
(x-2)^2 + (y+3)^2 = 25
(x+2)^2 + (y-3)^2 = 25
(x-2)^2 + (y-3)^2 = 25
(x+2)^2 + (y+3)^2 = 25
Explanation - Equation of circle: (x-h)^2 + (y-k)^2 = r^2. Here, h=2, k=-3, r=5 => (x-2)^2 + (y+3)^2 = 25
Correct answer is: (x-2)^2 + (y+3)^2 = 25
Q.12 If a line divides the line segment joining points A(1, 2) and B(7, 8) in the ratio 2:1, the coordinates of the point are:
(5, 6)
(3, 4)
(4, 5)
(6, 7)
Explanation - Section formula: ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)) => ((2*7+1*1)/3, (2*8+1*2)/3) = (15/3, 18/3) = (5,6)
Correct answer is: (4, 5)
Q.13 Find the slope of the line joining the points (2, 3) and (-4, 1).
1/3
1/2
-1/3
-1/2
Explanation - Slope m = (1-3)/(-4-2) = (-2)/(-6) = 1/3
Correct answer is: -1/2
Q.14 The equation of the line passing through (0, 0) and having slope 4 is:
y = 4x
y = x/4
y = -4x
y = 4
Explanation - Line equation using slope-intercept: y = mx + c, c=0 => y = 4x
Correct answer is: y = 4x
Q.15 The x-intercept of the line 3x - 4y + 12 = 0 is:
4
-4
3
-3
Explanation - x-intercept: put y=0 => 3x +12 =0 => x=-4
Correct answer is: 4
Q.16 The y-intercept of the line 2x + 5y - 10 = 0 is:
2
-2
5
-5
Explanation - y-intercept: put x=0 => 5y-10=0 => y=2
Correct answer is: -2
Q.17 The coordinates of the circumcenter of a triangle with vertices A(0,0), B(6,0), and C(0,8) are:
(3,4)
(3,0)
(0,4)
(2,3)
Explanation - Circumcenter is intersection of perpendicular bisectors. Midpoint AB=(3,0), perpendicular slope=∞, line x=3; Midpoint AC=(0,4), perpendicular slope=0, line y=4 => intersection (3,4)
Correct answer is: (3,4)
Q.18 If the distance between two points is zero, then:
Points are on the same line
Points coincide
Points are equidistant from origin
Points are perpendicular
Explanation - Distance zero implies the two points are identical.
Correct answer is: Points coincide
Q.19 The locus of a point equidistant from points A(0,0) and B(4,0) is:
x = 2
y = 2
y = x
x = y
Explanation - Equidistant points from A and B lie on perpendicular bisector of AB. Midpoint = (2,0), perpendicular bisector is vertical line x=2
Correct answer is: x = 2
Q.20 The distance between parallel lines 3x - 4y + 5 = 0 and 3x - 4y - 7 = 0 is:
12/5
1
√(12)
√5
Explanation - Distance formula between parallel lines |c1-c2|/√(a^2+b^2) = |5-(-7)|/√(3^2+(-4)^2)=12/5
Correct answer is: 12/5
Q.21 Equation of a line through (1,2) making 45° with x-axis is:
y = x + 1
y = x + 1
y = -x + 3
y = x + 2
Explanation - Slope m = tan(45°) = 1, y -2 =1(x-1)=> y=x+1 ? Wait compute: y-2=x-1 => y=x+1. Correct answer is y=x+1
Correct answer is: y = x + 2
Q.22 If the coordinates of a point are (x, y) and it lies on the line y = 2x + 3, then y - 2x equals:
3
-3
2
-2
Explanation - Given line equation y = 2x +3 => y-2x=3
Correct answer is: 3
Q.23 The line joining points (1,2) and (4,6) divides the line joining (0,0) and (7,8) in the ratio:
1:1
1:2
2:1
Cannot determine
Explanation - The line joining two points does not divide another line unless intersection point known, insufficient information.
Correct answer is: Cannot determine
Q.24 If a line passes through (3,4) and is parallel to y = 5x + 2, its equation is:
y = 5x - 11
y = 5x + 11
y = -1/5x + 4
y = 1/5x + 3
Explanation - Parallel slope m=5, pass through (3,4): y-4 =5(x-3) => y=5x-11
Correct answer is: y = 5x - 11
Q.25 The equation of the line joining points (2,3) and (2,7) is:
x=2
y=2
y=x
y=-x
Explanation - Vertical line passing through x=2
Correct answer is: x=2
Q.26 If (x,y) lies on x^2 + y^2 = 25, the distance from origin is:
5
25
√25
0
Explanation - Distance from origin = √(x^2 + y^2) = √25 =5
Correct answer is: 5