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Punjab (PTB) · Chapter test · Free

2nd Year Mathematics Chapter 5 TestUNIT 5: ANALYTICAL GEOMETRY

22 marks · 40 minutes · 18 questions. Covers: UNIT 5: ANALYTICAL GEOMETRY.

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2nd Year Mathematics Chapter 5 Test

2nd Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 22Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. The separate linear equations for the pair of lines  are:

    1. 6x+y=0 and x-4y=0

    2. 2x+y=0 and 3x-4y=0

    3. 2x-y=0 and 3x+4y=0

    4. 3x+y=0 and 2x-4y=0

  2. The point where all three medians of a triangle intersect each other is called the:

    1. Orthocenter

    2. Circumcenter

    3. Incenter

    4. Centroid

  3. Who first developed analytical geometry in the 17th century?

    1. Isaac Newton

    2. René Descartes

    3. Pythagoras

    4. Euclid

  4. In a triangle PQR with vertices P(1, 2), Q(5, -6), and R(7, -2), what are the coordinates of the midpoint of side QR through which the median from P passes?

    1. (3,-4)

    2. (6,-2)

    3. (6,-4)

    4. (1,-4)

  5. The coordinates of the midpoint of the line segment joining P(1, -2) and Q(5, 4) are:

    1. (2,2)

    2. (3,1)

    3. (3,3)

    4. (6,2)

  6. Analytical geometry is also known as:

    1. Algebra

    2. Coordinate geometry

    3. Topology

    4. Calculus

  7. What is the joint equation of lines passing through the origin and perpendicular to the lines ?

    1. 2x2+5xy-3y2=0

    2. 3x2+5xy-3y2=0

    3. 2x2-5xy-3y2=0

    4. 2x2+5xy+3y2=0

  8. What is the distance between the points A(2,3) and B(5,7):

    1. 3 units

    2. 4 units

    3. 5 units

    4. 7 units

  9. If theree lines  are concurrent, which condition must their coefficients satisfy?

    1. C1(m2-m3)+c2(m3-m1)+c3(m1-m2)=0

    2. C1(m-m3)+c2(m3-m1)+c3(m1-m2)=0

    3. C1(m2-m3)+c2(m-m1)+c3(m1-m)=0

    4. C(m2-m3)+c2(m3-m1)+c3(m1-m)=0

  10.  By computing the area of a triangle, if the area comes out to be 0, then the given three points are:

    1. Equidistant

    2. Collinear

    3. Non-collinear

    4. Vertices of a right-angled triangle

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Define analytical geometry.

  2. Write down an equation of the straight line which cuts the x-axis at (3,0) and y-axis (0,-6).

  3. Write the practical applications of analytical geometry.

  4. Triangle ABC has vertices A(2,3), B(4,5) and C(-2,7). Find the equations of medians of the triangle ABC.

  5. The vertices of  are P(1,2), Q(5,-6) and R(7,-2). Find the equation of all three medians.

  6. Convert the following equation into: x-2y+4=0 (i) Slope intercept form (ii) Two point form (iii) Intercept form (iv) Point slope form (v) Normal form (vi) Symmetric form.

  7. Convert the following equation into: 4x+5y-20=0 (i) Slope intercept form (ii) Two point form (iii) Intercept form (iv) Point slope form (v) Normal form (vi) Symmetric form.

  8. Show that the medians of the triangle with vertices A(3,2), B(-1,-5) and C(7,2) are concurrent.