(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

The point P (5, 3) was reflected in the origin to get the image P’.

1. Write down the co-ordinates of P’.
2. If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.
3. If N is the foot of the perpendicular from P’ to the x-axis, find the co-ordinates of N.
4. Name the figure PMP’N.
5. Find the area of the figure PMP’N.

The point P (3, 4) is reflected to P’ in the x-axis; and O’ is the image of O (the origin) when reflected in the line PP’. Write:

1. the co-ordinates of P’ and O’.
2. the length of the segments PP’ and OO’.
3. the perimeter of the quadrilateral POP’O’.
4. the geometrical name of the figure POP’O’.

A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A’, B’, C’ and D’ respectively. Locate A’, B’, C’ and D’ on the graph sheet and write their co-ordinates. Are D, A, A’ and D’ collinear?

P and Q have co-ordinates (0, 5) and (–2, 4).

1. P is invariant when reflected in an axis. Name the axis.
2. Find the image of Q on reflection in the axis found in (a).
3. (0, k) on reflection in the origin is invariant. Write the value of k.
4. Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

The triangle ABC, where A is (2, 6), B is (–3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A"B"C".

1. Write down the co-ordinates of A", B" and C".
2. Write down a single transformation that maps triangle ABC onto triangle A"B"C".

1. The point P (2, –4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.
2. The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
3. Name the figure PQR.
4. Find the area of figure PQR.

A’ and B’ are images of A (-3, 5) and B (-5, 3) respectively on reflection in y-axis. Find: (

a) the co-ordinates of A’ and B’.

(b) Assign special name of quadrilateral AA’B’B.

(c) Are AB’ and BA’ equal in length?

Using a graph paper, plot the point A (6, 4) and B (0, 4).

(a) Reflect A and B in the origin to get the image A’ and B’.

(b) Write the co-ordinates of A’ and B’.

(c) Sate the geometrical name for the figure ABA’B’.

(d) Find its perimeter.

On a graph paper, draw the lines x = 3 and y = –5. Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.

On a graph paper, draw the line x = 6. Now, on the same graph paper, draw the locus of the point which moves in such a way that its distantce from the given line is always equal to 3 units 

Describe the locus of vertices of all isosceles triangles having a common base.

Describe the locus of a point in space, which is always at a distance of 4 cm from a fixed point.  

Describe the locus of a point P, so that:

AB² = AP² + BP²,

where A and B are two fixed points.

Angle ABC = 60° and BA = BC = 8 cm. The mid-points of BA and BC are M and N respectively. Draw and describe the locus of a point which is:

1. equidistant from BA and BC.
2. 4 cm from M.
3. 4 cm from N.
   Mark the point P, which is 4 cm from both M and N, and equidistant from BA and BC. Join MP and NP, and describe the figure BMPN.

O is a fixed point. Point P moves along a fixed line AB. Q is a point on OP produced such that OP = PQ. Prove that the locus of point Q is a line parallel to AB.

Draw an angle ABC = 75°. Find a point P such that P is at a distance of 2 cm from AB and 1.5 cm from BC.

Construct a triangle ABC, with AB = 5.6 cm, AC = BC = 9.2 cm. Find the points equidistant from AB and AC; and also 2 cm from BC. Measure the distance between the two points obtained. 

Construct a triangle ABC, with AB = 6 cm, AC = BC = 9 cm. Find a point 4 cm from A and equidistant from B and C. 

Ruler and compasses may be used in this question. All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.

1. Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and angle ABC = 60°.
2. Construct the locus of all points inside triangle ABC, which are equidistant from B and C.
3. Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.
4. Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
5. Measure and record the length of CQ.

State the locus of a point in a rhombus ABCD, which is equidistant

1. from AB and AD;
2. from the vertices A and C.