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

The points P (4, 1) and Q (–2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

A point P (–2, 3) is reflected in line x = 2 to point P’. Find the co-ordinates of P’.

A point P (a, b) is reflected in the x-axis to P’ (2, –3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:

1. A’ of A under reflection in the x-axis.
2. B’ of B under reflection in the line AA’.
3. A” of A under reflection in the y-axis.
4. B” of B under reflection in the line AA”.

1. Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
2. A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.
3. B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.
4. Write down the geometrical name of the figure AA’BB’.
5. Name the invariant points under reflection in the x-axis.

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.