CBSE Board Half Yearly Exam Question Paper Class-X Coordinate Geo Math 2022

ABC School

SUBJECT: MATHEMATICS

CLASS : X

CBSE Board Half Yearly Exam Question Paper

NO. OF BLOCKS: 6

TOPIC: COORDINATE GEOMETRY

SUBTOPICS:-

i) Distance formula to calculate the distance between any two points in a plane.

ii) Section formula to find the coordinates of a point which divides the line segment joining two points (x1,y1) and (x2,y2) in the ratio m:n.

iii) Area of a triangle formed by joining vertices (x1,y1), (x2,y2 ) and (x3, y3 ) 

INSTRUCTIONAL AIDS:-Presentation by screen sharing, offline whiteboard, online whiteboard, 

You tube links, E-lesson

LEARNING OUTCOMES:- Each student will be able to

● To learn distance formula

● To learn section formula

● To apply the distance formula, section formula in solving problems

● To apply the knowledge of coordinate geometry in daily

Block 1

Lesson Development

In Class IX, you have studied that to locate the position of a point on a plane, we require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate, or abscissa. The distance of a point from the x-axis is called its

y-coordinate, or ordinate. The coordinates of a point on the x-axis are of the form (x, 0), and of a point on the y-axis are of the form (0, y)

DISTANCE FORMULA –

Assignment : Questions marked with red circles are H.W questions are to be done in the Maths register.

Project based on :.Use of coordinate Geometry in Air Transport.

Maths Lab Activities based on .Distance formula

Examplar Questions:

Question 1:

The distance of the point P(2, 3) from the X-axis is

(a) 2 (b) 3 (c) 1 (d) 5

Question 2: 

The distance of the point P(- 6, 8) from the origin is

(a) 8 (b) 2√7 (c) 10 (d) 6

Question 3:

If AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0), then the length of its diagonal is

(a) 5 (b) 3 (c) √34 (d) 4

Question 4:

If the point P(2,1) lies on the line segment joining points A(4, 2) and 6(8, 4), then

(a)AP =⅓ AB  (b) AP = PB  (c)PB =⅓ AB  (d)AP =½ AB

Question 5:

The coordinates of the point which is equidistant from the three vertices of the ΔAOB as

shown in the figure is

Question 6:

A circle has its centre at the origin and a point P (5, 0) lies on it. The point Q (6, 8) lies outside the circle.State true or false

Block 2

Lesson Development

Section Formula

Let (– 4, 6)divide AB internally in the ratio k : 1. Using the section formula, we get

Centroid of a triangle

Examplar Questions:

Question 1:

The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1: 2 internally lies in the

(a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant

Question 2: 

The point which lies on the perpendicular bisector of the line segment joining the points A(-2, – 5) and B(2, 5) is

(a) (0,0) (b) (0, 2) (c) (2, 0) (d)(-2,0)

Question 3: 

The fourth vertex D of a parallelogram ABCD whose three vertices are A(- 2, 3), B(6, 7) and C(8, 3) is

(a) (0,1) (b) (0,-1) (c) (-1,0) (d) (1,0)

Question 4: 

The perpendicular bisector of the line segment joining the points A(1,5) and 8(4,6) cuts the y-axis at

(a) (0,13) (b) (0,-13) (c) (0,12) (d) (13,0)

Question 5: 

A line intersects the y-axis and X-axis at the points P and Q, respectively. If (2, – 5) is the mid-point of PQ, then the coordinates of P and Q are, respectively

(a) (0,-5) and (2, 0) (b) (0, 10) and (- 4, 0) 

(c) (0, 4) and (- 10, 0) (d) (0, – 10) and (4, 0)

Question 6: 

If P(9a -2, – b) divides line segment joining A(3a + 1,-3) and B(8a, 5) in the ratio 3 : 1, then find the values of a and b.

EXERCISE 7.4 (Optional)*

1. Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).

3. Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).

4. The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the other two vertices.

5. The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the Fig.

7.14. The students are to sow seeds of flowering plants on the remaining area of the plot.

(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?

6 . Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ ABC.

(i) The median from A meets BC at D. Find the coordinates of the point D.

(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1

(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.

(iv) (iv) What do yo observe? [Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2 : 1.]

(v) If A(x1 , y1), B(x2 , y2) and C(x3, y3 ) are the vertices of Δ ABC, find the coordinates of the centroid of the triangle. 8. ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.

SUMMARY

Art Integration Activity

Refer to the Following link for the Art integration activity

Case study questions: 

CASE STUDY 1:

Download PDF Here

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