Every Book Back multiple-choice question from Coordinate Geometry (10th Standard Mathematics, Samacheer Kalvi) — each with the correct option highlighted and a clear, worked explanation. Free to read in English and Tamil.
Q1
The area of triangle formed by the points (-5,0), (0,-5) and (5,0) is
- A. 0 sq.units
- B. 25 sq.unitsCorrect
- C. 5 sq.units
- D. none of these
Explanation. The area of a triangle with vertices (-5,0), (0,-5), and (5,0) is calculated using the formula 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. Substituting the coordinates yields 25 square units.
Q2
A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is
- A. x = 10Correct
- B. y = 10
- C. x = 0
- D. y = 0
Explanation. Since the wall represents the Y-axis (where x = 0), any path maintained at a constant distance of 10 units parallel to the wall is represented by the equation x = 10.
Q3
The straight line given by the equation x = 11 is
- A. parallel to X axis
- B. parallel to Y axisCorrect
- C. passing through the origin
- D. passing through the point (0,11)
Explanation. The equation x = 11 represents a line where the x-coordinate of every point is constant. This form of equation always represents a straight line parallel to the Y-axis.
Q4
If (5,7), (3,p) and (6,6) are collinear, then the value of p is
- A. 3
- B. 6
- C. 9Correct
- D. 12
Explanation. For three points to be collinear, the slope between the first two must equal the slope between the last two. Solving (p - 7)/(3 - 5) = (6 - p)/(6 - 3) yields p = 9.
Q5
The point of intersection of 3x - y = 4 and x + y = 8 is
- A. (5,3)
- B. (2,4)
- C. (3,5)Correct
- D. (4,4)
Explanation. Solving the system of simultaneous equations 3x - y = 4 and x + y = 8 by adding them gives 4x = 12, so x = 3. Substituting x = 3 into x + y = 8 gives y = 5.
Q6
The slope of the line joining (12, 3), (4, a) is 1/8. The value of 'a' is
- A. 1
- B. 4
- C. -5
- D. 2Correct
Explanation. The slope is defined as (y2 - y1) / (x2 - x1). Setting (a - 3) / (4 - 12) equal to 1/8 gives (a - 3) / -8 = 1/8. Solving for a yields a = 2.
Q7
The slope of the line which is perpendicular to a line joining the points (0,0) and (-8,8) is
- A. -1
- B. 1Correct
- C. 1/3
- D. -8
Explanation. The slope of the line joining (0,0) and (-8,8) is (8 - 0)/(-8 - 0) = -1. The slope of a perpendicular line is the negative reciprocal, which is -1/(-1) = 1.
Q8
If slope of the line PQ is 1/3 then slope of the perpendicular bisector of PQ is
- A. 3
- B. -3Correct
- C. 1/3
- D. 0
Explanation. The product of the slopes of two perpendicular lines is always -1. Since the slope of PQ is 1/3, the slope of its perpendicular bisector is -1 / (1/3) = -3.
Q9
If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is
- A. 8x + 5y = 40Correct
- B. 8x - 5y = 40
- C. x = 8
- D. y = 5
Explanation. The intercept form of a straight line is x/a + y/b = 1. Here, the x-intercept a is 5 and the y-intercept b is 8. Substituting these values gives x/5 + y/8 = 1, which simplifies to 8x + 5y = 40.
Q10
The equation of a line passing through the origin and perpendicular to the line 7x - 3y + 4 = 0 is
- A. 7x - 3y + 4 = 0
- B. 3x - 7y + 4 = 0
- C. 3x + 7y = 0Correct
- D. 7x - 3y = 0
Explanation. A line perpendicular to 7x - 3y + 4 = 0 is of the form 3x + 7y + k = 0. Since it passes through the origin (0,0), the constant k is 0, giving the equation 3x + 7y = 0.
Q11
Consider four straight lines (i) l1 : y = 3/4 x + 5, (ii) l2 : y = 4/3 x - 1, (iii) l3 : y + 3/4 x = 7, (iv) l4 : x + 4/3 y = 2. Which of the following statement is true?
- A. l1 and l2 are perpendicular
- B. l1 and l4 are parallel
- C. l2 and l4 are perpendicularCorrect
- D. l2 and l3 are parallel
Explanation. The slope of line l2 is 4/3. The line l4 is x + 4/3 y = 2, which has a slope of -3/4. Since the product of their slopes is -1, the lines are perpendicular.
Q12
A straight line has equation 8y = 4x + 21. Which of the following is true
- A. The slope is 0.5 and the y intercept is 2.6Correct
- B. The slope is 5 and the y intercept is 1.6
- C. The slope is 0.5 and the y intercept is 1.6
- D. The slope is 5 and the y intercept is 2.6
Explanation. Rewriting the equation 8y = 4x + 21 in slope-intercept form y = mx + c gives y = 0.5x + 2.625. Thus, the slope is 0.5 and the y-intercept is approximately 2.6.
Q13
When proving that a quadrilateral is a trapezium, it is necessary to show
- A. Two sides are parallel
- B. Two parallel and two non-parallel sidesCorrect
- C. Opposite sides are parallel
- D. All sides are of equal length
Explanation. To prove a quadrilateral is a trapezium, it is necessary to show that one pair of opposite sides is parallel while the other pair is non-parallel.
Q14
When proving that a quadrilateral is a parallelogram by using slopes you must find
- A. The slopes of two sides
- B. The slopes of two pair of opposite sidesCorrect
- C. The lengths of all sides
- D. Both the lengths and slopes of two sides
Explanation. To prove that a quadrilateral is a parallelogram using slopes, you must demonstrate that both pairs of opposite sides are parallel by showing their respective slopes are equal.
Q15
(2, 1) is the point of intersection of two lines.
- A. x - y - 3 = 0; 3x - y - 7 = 0
- B. x + y = 3; 3x + y = 7Correct
- C. 3x + 3y = 7; x + y = 3
- D. x + y - 3 = 0; 3x - y - 7 = 0
Explanation. Substituting the point (2, 1) into x + y = 3 gives 2 + 1 = 3, which is true. Substituting it into 3x + y = 7 gives 3(2) + 1 = 7, which is also true.
