10th Maths Unit 5 Important 5 Mark Questions

Boost your board exam scores by mastering the 10th Maths Unit 5 Important 5 Marks questions. Coordinate Geometry (ஆயத்தொலை வடிவியல்) is a scoring and crucial chapter, regularly featuring high-weightage problems on finding the area of a quadrilateral, verifying collinearity, finding the equation of a straight line, and working with perpendicular or parallel line conditions. This curated selection brings you the most frequently asked 5-mark problems and expected compulsory questions, enabling you to step into your mathematics exam with complete clarity and confidence.

UNIT - 5 (CO-ORDINATE GEOMETRY)

IMPORTANT FIVE MARKS QUESTIONS

1. Find the area of the quadrilateral whose vertices are (-9, -2), (-8, -4), (2, 2), and (1, -3).

2. Find the area of the quadrilateral whose vertices are (-9, 0), (-8, 6), (-1, -2), and (-6, -3).

3. Find the area of the quadrilateral whose vertices are (8, 6), (5, 11), (-5, 12), (-4, 3).

4. Find the value of k, if the area of quadrilateral is 28 sq.units, whose vertices are taken in the order (-4, -2), (-3, k), (3, -2), and (2, 3).

5. If the points A(-3, 9), B(a, b) and C(4, -5) are collinear and if a + b = 1, then find a and b.

6. The line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

7. If the points A(2, 2), B(-2, -3), C(1, -3) and D(x, y) form a parallelogram then find the value of x and y.

8. A mobile phone is put to use when the battery power is 100%. The percent of battery power y (in decimal) remaining after using the mobile phone for x hours is assumed as y = -0.25x + 1.
(i) Find the number of hours elapsed if the battery power is 40%.
(ii) How much time does it take so that the battery has no power?

9. A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3, 8). Find its equation.

10. You are downloading a song. The percent y (in decimal form) of megabytes remaining to get downloaded in x seconds is given by y = -0.1x + 1.
(i) find the total MB of the song.
(ii) after how many seconds will 75% of the song get downloaded?
(iii) after how many seconds the song will be downloaded completely?

11. Find the equation of a straight line:
(i) passing through (1, -4) and has intercepts which are in the ratio 2:5
(ii) passing through (-8, 4) and making equal intercepts on the coordinate axes

12. If the vertices of a ΔABC are A(6, 2), B(-5, -1) and C(1, 9):
(i) find the equation of median
(ii) find the equation of altitude

13. Find the equation of a straight line parallel to Y axis and passing through the point of intersection of the lines 4x + 5y = 13 and x - 8y + 9 = 0.

14. Find the equation of a line passing through (6, -2) and perpendicular to the line joining the points (6, 7) and (2, -3).

15. Find the equation of a straight line through the intersection of lines 7x + 3y = 10, 5x - 4y = 1 and parallel to the line 13x + 5y + 12 = 0.

16. Find the equation of a straight line through the intersection of lines 5x - 6y = 2, 3x + 2y = 10 and perpendicular to the line 4x - 7y + 13 = 0.

17. Find the equation of a straight line joining the point of intersection of 3x + y + 2 = 0 and x - 2y - 4 = 0 to the point of intersection of 7x - 3y = -12 and 2y = x + 3.

S. ANITHA M.Sc., M.Ed., MATHEMATICS

UNIT - 4 (GEOMETRY) IMPORTANT FIVE MARKS

1. State and prove Basic Proportionality Theorem (BPT) or Thales theorem Statement.

2. State and prove Angle Bisector Theorem (ABT).

3. State and prove Pythagoras Theorem or Baudhayana Theorem.

4. An insect 8 m away initially from the foot of a lamp post which is 6 m tall, crawls towards it moving through a distance. If its distance from the top of the lamp post is equal to the distance it has moved, how far is the insect away from the foot of the lamp post?

5. P and Q are the mid-points of the sides CA and CB respectively of a ΔABC, right angled at C. Prove that 4(AQ² + BP²) = 5AB².

6. The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle.

7. In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE² = 3AC² + 5AD².