Q.1 What is the distance between the points (3,4) and (0,0)?
3
4
5
7
Explanation - The distance formula is √((x2−x1)² + (y2−y1)²). Substituting values: √((3-0)² + (4-0)²) = √(9+16) = √25 = 5.
Correct answer is: 5
Q.2 What is the midpoint of the line joining (2,6) and (4,10)?
(3,8)
(6,16)
(2,10)
(4,6)
Explanation - The midpoint formula is ((x1+x2)/2, (y1+y2)/2). So midpoint = (2+4)/2, (6+10)/2 = (3,8).
Correct answer is: (3,8)
Q.3 If the slope of a line is 2, which of the following could be its equation?
y = 2x + 3
y = -x + 1
y = 3x - 2
y = -2x
Explanation - The slope-intercept form is y = mx + c, where m is the slope. Only option y = 2x + 3 has slope 2.
Correct answer is: y = 2x + 3
Q.4 The x-coordinate of the centroid of triangle with vertices (0,0), (6,0), (0,6) is:
0
2
3
4
Explanation - The centroid formula is ((x1+x2+x3)/3, (y1+y2+y3)/3). Here, (0+6+0)/3 = 2.
Correct answer is: 2
Q.5 What is the slope of the line joining points (2,3) and (4,7)?
1
2
4
0.5
Explanation - Slope = (y2−y1)/(x2−x1) = (7−3)/(4−2) = 4/2 = 2.
Correct answer is: 2
Q.6 Equation of x-axis is:
x=0
y=0
x=y
y=x+1
Explanation - On the x-axis, the y-coordinate is always 0. Hence equation is y=0.
Correct answer is: y=0
Q.7 Equation of y-axis is:
y=0
x=0
x=y
y=x-1
Explanation - On the y-axis, the x-coordinate is always 0. Hence equation is x=0.
Correct answer is: x=0
Q.8 The line passing through (0,0) and (2,2) has slope:
0
1
2
-1
Explanation - Slope = (y2−y1)/(x2−x1) = (2−0)/(2−0) = 1.
Correct answer is: 1
Q.9 The point (3, -2) lies in which quadrant?
I
II
III
IV
Explanation - Since x > 0 and y < 0, the point lies in the 4th quadrant.
Correct answer is: IV
Q.10 The distance between points (1,2) and (4,6) is:
3
5
6
7
Explanation - Using distance formula: √((4−1)² + (6−2)²) = √(9+16) = √25 = 5.
Correct answer is: 5
Q.11 Equation of the line parallel to y = 3x + 2 and passing through (0,5) is:
y=3x+5
y=3x-5
y=-3x+5
y=2x+5
Explanation - Parallel lines have the same slope. Since slope is 3, equation is y=3x+c. Substituting (0,5): 5=3*0+c ⇒ c=5. So y=3x+5.
Correct answer is: y=3x+5
Q.12 Slope of a line perpendicular to y = -1/2 x + 3 is:
2
-2
1/2
-1/2
Explanation - If slope of one line is m, perpendicular line’s slope = -1/m. Here m = -1/2 ⇒ slope = 2.
Correct answer is: 2
Q.13 The coordinates of origin are:
(0,0)
(1,0)
(0,1)
(1,1)
Explanation - Origin is the intersection of x and y axes. Coordinates are (0,0).
Correct answer is: (0,0)
Q.14 What is the length of the line segment joining (7,1) and (3,4)?
4
5
6
7
Explanation - Distance = √((7−3)² + (1−4)²) = √(16+9) = √25 = 5.
Correct answer is: 5
Q.15 Equation of a line with slope 4 passing through (0,0) is:
y=4x
y=x+4
y=4x+1
y=x-4
Explanation - Equation of line through origin: y=mx. Here slope m=4, so equation is y=4x.
Correct answer is: y=4x
Q.16 The centroid of a triangle divides each median in ratio:
1:1
2:1
1:2
3:1
Explanation - The centroid divides each median in the ratio 2:1, with longer part towards the vertex.
Correct answer is: 2:1
Q.17 If a line passes through (2,3) and slope is 3, what is its equation?
y=3x+2
y=3x-3
y=3x-3
y=3x-3
Explanation - Equation: y−y1 = m(x−x1). Substituting: y−3 = 3(x−2). Simplify: y=3x−3.
Correct answer is: y=3x-3
Q.18 Which point lies on the line y=2x+1?
(1,2)
(2,5)
(3,4)
(0,0)
Explanation - Substitute x=2: y=2(2)+1=5. So point (2,5) lies on the line.
Correct answer is: (2,5)
Q.19 What is the slope of line y=7?
0
undefined
7
1/7
Explanation - Equation y=constant represents a horizontal line with slope 0.
Correct answer is: 0
Q.20 What is the slope of line x=3?
0
3
undefined
1/3
Explanation - Equation x=constant is a vertical line whose slope is undefined.
Correct answer is: undefined
Q.21 If a line passes through (0,2) and (2,0), what is its slope?
1
-1
2
-2
Explanation - Slope = (0−2)/(2−0) = -2/2 = -1.
Correct answer is: -1
Q.22 The point (0,5) lies on which axis?
X-axis
Y-axis
Origin
None
Explanation - Since x=0, the point lies on the y-axis.
Correct answer is: Y-axis
Q.23 Which quadrant does point (-2, -3) lie in?
I
II
III
IV
Explanation - Both x and y are negative, so point lies in 3rd quadrant.
Correct answer is: III
Q.24 Equation of line with slope 1 and passing through origin is:
y=x
y=-x
y=1
x=1
Explanation - Equation through origin with slope m is y=mx. Substituting m=1, y=x.
Correct answer is: y=x
Q.25 The coordinates of a point dividing line joining (2,2) and (8,8) in ratio 1:2 internally are:
(4,4)
(6,6)
(8,8)
(2,2)
Explanation - Formula: (mx2+nx1)/(m+n), (my2+ny1)/(m+n). With ratio 1:2 ⇒ point = (1*8+2*2)/3 , (1*8+2*2)/3 = (12/3,12/3) = (4,4).
Correct answer is: (4,4)