Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) In which quadrant does the point (-2, 3) lie?

Perfect! Second quadrant has (-x, +y) coordinates.

(2) Write the coordinates of the point which lies on both the x-axis and y-axis.

The point where both axes intersect: (Enter it in the format of a,b)

Correct! The origin (0, 0) is the only point on both axes.

(3) What is the y-coordinate of a point lying on the x-axis?

Points on x-axis have y-coordinate:

Perfect! All points on x-axis have y = 0.

(4) State the formula for the section formula (internal division).

For point dividing line joining (x1, y1) and (x2, y2) in ratio m : n

Point =

Excellent! This is the internal section formula.

Short Answer Questions (2 Marks Each)

Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.

(1) Find the distance between the points A(-1, -2) and B(3, 1). d =

Perfect! Distance between A and B is 5 units.

(2) Find the coordinates of the midpoint of the line segment joining A(-4, 5) and B(2, -3).

Midpoint formula: (Enter it in the format of a,b)

Excellent! The midpoint is (-1, 1).

(3) The coordinates of the midpoint of a line segment are (1, 2). If one end is (3, 4), find the other end.

Other end: (Enter it in the format of a,b)

Perfect! The other endpoint is (-1, 0).

(4) A line segment has endpoints at (2, -1) and (8, 5). Find its length.

Correct! Length = 62 units ≈ 8.49 units.

Long Answer Questions (4 Marks Each)

Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.

(1) Find the point which divides the line joining the points A(2, 3) and B(6, 7) in the ratio 2:3.

The dividing point is:

Excellent! The point is (185, 235) or (3.6, 4.6).

(2) Show that the points A(1, 1), B(4, 4), C(7, 7) are collinear.

Method: Three points are collinear if they lie on the same straight line.

Slope of AB: m1 =

Slope of BC: m2 =

Slope of AC: m3 =

Since m1 = m2 = m3 = 1, all slopes are

Conclusion: The points A, B, C are

Perfect! Equal slopes prove the points are collinear.

(3) A triangle has vertices at A(2, 3), B(6, 7), C(4, -3). Find the lengths of all sides and determine whether it is an isosceles triangle.

Side AB: |AB| =

Side BC: |BC| =

Side AC: |AC| =

Since all three sides have lengths, the triangle is .

Excellent analysis! All sides are different, so it's a scalene triangle.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The distance between the points (-1, 2) and (2, 6) is:

(a) 3 (b) 4 (c) 5 (d) 6

Correct! d = 2−−12+6−22 = 9+16 = 25 = 5.

(2) The midpoint of the line joining (-2, 4) and (4, -2) is:

(a) (1, 1) (b) (0, 0) (c) (3, -3) (d) (2, 1)

(1, 1)

(0, 0)

(3, -3)

(2, 1)

Correct! Midpoint = (−2+42, 4+−22) = (1, 1).

(3) If a point lies on the y-axis, its x-coordinate is:

(a) x (b) y (c) 0 (d) 1

Correct! All points on y-axis have x-coordinate = 0.

(4) Section formula (internal) gives the point dividing a line joining A(x1, y1) and B(x2, y2) in the ratio m:n as:

(a) (x1+x22, y1+y22) (b) (mx2+nx1m+n, my2+ny1m+n) (c) (x1 + x2, y1 + y2) (d) (mx1+nx2m+n, my1+ny2m+n)

((x_1+x_2)/2, (y_1+y_2)/2)

((mx_2 + nx_1)/(m+n), (my_2 + ny_1)/(m+n))

(x_1 + x_2, y_1 + y_2)

((mx_1 + nx_2)/(m+n), (my_1 + ny_2)/(m+n))

Correct! This is the standard section formula for internal division.

(5) Coordinates of the point dividing the line joining (0, 0) and (6, 6) in the ratio 1:2 are:

(a) (2, 2) (b) (3, 3) (c) (4, 4) (d) (5, 5)

(2, 2)

(3, 3)

(4, 4)

(5, 5)

Correct! Using section formula: (1×6+2×03, 1×6+2×03) = (2, 2).

(6) The point (-4, -3) lies in:

(a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

Correct! Both coordinates are negative, so it's in the third quadrant.

(7) Which of the following is NOT a correct coordinate for a point in the second quadrant?

(a) (-3, 5) (b) (-2, -3) (c) (-1, 4) (d) (-5, 6)

(-3, 5)

(-2, -3)

(-1, 4)

(-5, 6)

Correct! (-2, -3) has both negative coordinates, so it's in the third quadrant, not second.

(8) The coordinates of the centroid of triangle with vertices A(1, 1), B(4, 4), C(7, 1) are:

(a) (4, 2) (b) (2, 2) (c) (3, 2) (d) (4, 3)

(4, 2)

(2, 2)

(3, 2)

(4, 3)

Correct! Centroid = (1+4+73, 1+4+13) = (123, 63) = (4, 2).

(9) What is the slope of the line joining (0, 0) and (3, 3)?

(a) 0 (b) 1 (c) 2 (d) 3

Correct! Slope = 3−03−0 = 33 = 1.

(10) If the distance between points (x, 0) and (0, 0) is 5, what is the value of x?

(a) 5 (b) -5 (c) ±5 (d) 25

-5

±5

Correct! Distance = x−02+0−02 = |x| = 5, so x = ±5.

Finding the point exactly between two locations

Finding the point that divides a line segment in a given ratio

Finding the area of a triangle formed by three points

Locating the center of a line segment

Finding coordinates dividing a line internally in the ratio 3:2

Calculating region covered by 3 coordinate points

Used to find average of x and y coordinates

Used when ratio is involved between two endpoints

Area = 1/2 |x_1(y_2−y_3) + x_2(y_3−y_1) + x_3(y_1−y_2)|

Midpoint Applications

Section Formula Applications

Area of Triangle Applications

Coordinate Geometry Challenge

Determine whether these statements about coordinate geometry are True or False:

The origin lies in the first quadrant

Points on the x-axis have positive y-coordinates

The midpoint of a line segment is equidistant from both endpoints

The distance formula is derived from the Pythagorean theorem

All points in the second quadrant have positive x-coordinates

Collinear points have the same slope between any two pairs

Chapter 7: Coordinate Geometry

Glossary

Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

Short Answer Questions (2 Marks Each)

Long Answer Questions (4 Marks Each)

Part B: Objective Questions (1 Mark Each)

Coordinate Geometry Challenge

Coordinate Geometry Quiz

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Chapter 7: Coordinate Geometry

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Glossary

Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

Short Answer Questions (2 Marks Each)

Long Answer Questions (4 Marks Each)

Part B: Objective Questions (1 Mark Each)

Coordinate Geometry Challenge

Coordinate Geometry Quiz