Coordinate Geometry quiz

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

The distance between the points (2, 3) and (4, 1) is:

The midpoint of the line segment joining (2, 3) and (8, 7) is:

The point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3 : 1 internally is:

The point on the y-axis has coordinates of the form:

The ratio in which the y-axis divides the line segment joining (5, -6) and (-1, -4) is:

If the centre of a circle is (2, -3) and one end of a diameter is (1, 4), the other end is:

The points (5, -2), (6, 4) and (7, -2) are the vertices of:

The perpendicular distance of the point (3, -4) from the x-axis is:

Points A(3, 1), B(6, 4) and C(8, 6) are:

Find the distance between the points (-5, 7) and (-1, 3). (2 marks)

Show that the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle. (2 marks)

Town B is located 36 km east and 15 km north of town A. Taking A as the origin, find the distance between the two towns. (2 marks)

Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3. (2 marks)

If A(-2, -2) and B(2, -4), find the coordinates of P on AB such that AP = (3/7) AB. (2 marks)

Find the value of k if the points A(2, 3), B(4, k) and C(6, -3) are collinear, using the fact that B is the midpoint of AC. (2 marks)

Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts. (2 marks)

If Q(0, 1) is equidistant from P(5, -3) and R(x, 6), find the values of x. (2 marks)

The midpoint of the segment joining A(2a, 4) and B(-2, 3b) is M(1, 2a + 1). Find a and b. (2 marks)

Find the point on the y-axis which is equidistant from A(6, 5) and B(-4, 3). (2 marks)

Find the area of the rhombus whose vertices, taken in order, are (3, 0), (4, 5), (-1, 4) and (-2, -1), after showing that it is a rhombus. (Hint: area of a rhombus = half the product of its diagonals) (3 marks)

Find the ratio in which the y-axis divides the line segment joining (5, -6) and (-1, -4). Also find the point of intersection. (3 marks)

The vertices of a triangle are A(4, 2), B(6, 5) and C(1, 4). The median from A meets BC at D. Find the coordinates of D, and find the coordinates of the point P on AD such that AP : PD = 2 : 1. (3 marks)

Show that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle. (3 marks)

If the point C(-1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B. (3 marks)

Read the passage and answer the questions. To conduct Sports Day activities in a rectangular school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD. Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th the distance AD on the 8th line and posts a red flag. Take AB as the x-axis and AD as the y-axis. (i) Write the coordinates of the green and red flags. (ii) Find the distance between the two flags. (iii) If Rashmi has to post a blue flag exactly halfway between the two flags, where should she post it? (5 marks)

Read the passage and answer the questions. A city map is drawn on a grid in which each unit represents 1 km. The railway station is at R(2, 3), the hospital at H(8, 11) and the bus stand at B(14, 3). (i) Find the distance between the railway station and the hospital. (ii) Is the hospital equidistant from the railway station and the bus stand? Show your working. (iii) A metro station is to be built at the midpoint of the road from R to B. Find its coordinates. (5 marks)

Read the passage and answer the questions. A straight pipeline is to be laid from a water tank T(1, -2) to a village V(9, 10), with distances in km. Pumping stations are to be placed so that the pipeline is divided into three equal parts. (i) In what ratios do the two pumping stations divide TV? (ii) Find the coordinates of the two pumping stations. (iii) Find the total length of the pipeline. (5 marks)

Read the passage and answer the questions. In an architect's plan of a garden, a triangular flower bed has corners at P(0, 0), Q(6, 0) and S(0, 8), with units in metres. A sprinkler is to be fixed at the midpoint M of the side QS. (i) Find the coordinates of M. (ii) Find the length of QS. (iii) Show that M is equidistant from P, Q and S, and state which property of right triangles this verifies. (5 marks)

Read the passage and answer the questions. A drone delivery company plots routes on a coordinate grid in km. A drone starts at A(-3, -1) and must reach B(9, 8), stopping at a charging point C that divides AB internally in the ratio 1 : 2. (i) Find the coordinates of C. (ii) Find the distance AB. (iii) How far does the drone travel from C to B? (5 marks)

Derive the distance formula for two points P(x1, y1) and Q(x2, y2) in the first quadrant, drawing the perpendiculars PR and QS to the x-axis and PT perpendicular to QS. Using the formula, find the point on the x-axis which is equidistant from (7, 6) and (3, 4). (6 marks)

Derive the section formula for the coordinates of the point P which divides the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2, using similar triangles. Draw the figure. Hence find the coordinates of the midpoint of the segment joining (-3, 10) and (6, -8). (6 marks)

Plot the points A(1, 7), B(4, 2), C(-1, -1) and D(-4, 4) on a graph and join them in order. Using the distance formula for sides and diagonals, determine whether ABCD is a square, and give reasons. (6 marks)

The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 1 : 2, and P lies on the line 3x - 18y + k = 0. Draw a rough figure, find the coordinates of P and the value of k. (6 marks)

Name the type of quadrilateral formed, if any, by the following points, giving reasons: (i) (-1, -2), (1, 0), (-1, 2), (-3, 0) (ii) (-3, 5), (3, 1), (0, 3), (-1, -4) (iii) (4, 5), (7, 6), (4, 3), (1, 2). Draw a rough sketch for each case. (6 marks)