Distance Formula & Graphing Quiz - ICSE Class 9 Mathematics

Free practice quiz: Distance Formula & Graphing (ICSE Class 9 Mathematics). 42 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. A line segment PQ has endpoints P(2, 5) and Q(8, 1). What are the coordinates of the midpoint M of PQ?

   1. (4, 3)
   2. (5, 3)
   3. (6, 2)
   4. (5, 4)
   Show answer

   Answer: B. (5, 3)

   The midpoint formula states that for two points (x1, y1) and (x2, y2), the midpoint coordinates are ((x1 + x2)/2, (y1 + y2)/2). Here, P(2, 5) and Q(8, 1). So, the midpoint M is ((2 + 8)/2, (5 + 1)/2) = (10/2, 6/2) = (5, 3).

2. What is the equation of the x-axis?

   1. x = 0
   2. y = 0
   3. x + y = 0
   4. y = x
   Show answer

   Answer: B. y = 0

   The x-axis is the horizontal line where the y-coordinate of every point is zero. Therefore, the equation of the x-axis is y = 0.

3. The distance between points (a, 2) and (3, 6) is 5. Find the possible values of 'a'.

   1. a = 6 or a = 0
   2. a = 5 or a = 1
   3. a = 7 or a = -1
   4. a = 6 or a = -1
   Show answer

   Answer: A. a = 6 or a = 0

   Using the distance formula: sqrt((3 - a)^2 + (6 - 2)^2) = 5. Squaring both sides: (3 - a)^2 + 4^2 = 5^2. (3 - a)^2 + 16 = 25. (3 - a)^2 = 9. So, 3 - a = 3 or 3 - a = -3. If 3 - a = 3, then a = 0. If 3 - a = -3, then a = 3 + 3 = 6. Thus, a = 6 or a = 0.

4. If point P(x, y) is equidistant from A(1, 2) and B(5, 6), what is the equation of the perpendicular bisector of AB?

   1. y = -x + 7
   2. y = x + 3
   3. y = -x + 6
   4. y = x + 4
   Show answer

   Answer: A. y = -x + 7

   First, find the midpoint of AB: M = ((1+5)/2, (2+6)/2) = (6/2, 8/2) = (3, 4). Next, find the slope of AB: m_AB = (6 - 2) / (5 - 1) = 4 / 4 = 1. The slope of the perpendicular bisector (m_perp) is the negative reciprocal of m_AB: m_perp = -1/1 = -1. Now, use the point-slope form with the midpoint M(3, 4) and slope m_perp = -1: y - 4 = -1(x - 3). y - 4 = -x + 3. y = -x + 3 + 4. y = -x + 7.

5. What is the x-coordinate of the point that divides the line segment joining A(-5, 3) and B(4, -7) in the ratio 2:7?

   1. -3
   2. -2
   3. -1
   4. 0
   Show answer

   Answer: A. -3

   Using the section formula for the x-coordinate: x = (m*x2 + n*x1) / (m+n). Here (x1, y1) = (-5, 3), (x2, y2) = (4, -7), m = 2, n = 7. x = (2*4 + 7*(-5)) / (2+7) = (8 - 35) / 9 = -27 / 9 = -3.

More quizzes

• Expansion and Factorization
• Probability
• Rectilinear Figures – Quadrilaterals
• Statistics – Data Presentation, Mean, Median
• Triangles – Theorems
• Trigonometric Ratios of Standard Angles

Browse all Mathematics quizzes