ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test

Ram

5 years ago

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test

Question 1.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). If the origin is the mid-point of the base BC, find the coordinates of the points A and B
Solution:

Question 2.
A and B have co-ordinates (4, 3) and (0, 1), Find
(i) the image A’ of A under reflection in the y-axis.
(ii) the image of B’ of B under reflection in the line AA’.
(iii) the length of A’B’.
Solution:

Question 3.
Find the co-ordinates of the point that divides the line segment joining the points P (5, -2) and Q (9, 6) internally in the ratio of 3 : 1.
Solution:

Question 4.
Find the coordinates of the point P which is three-fourths of the way from A (3, 1) to B (-2, 5).
Solution:

Question 5.
P and Q are the points on the line segment joining the points A (3, -1) and B (-6, 5) such that AP = PQ = QB. Find the co-ordinates of P and Q.
Solution:

Question 6.
The centre of a circle is (α + 2, α – 5). Find the value of a given that the circle passes through the points (2, -2) and (8, -2).
Solution:

Question 7.
The mid-point of the line joining A (2, p) and B (q, 4) is (3, 5). Calculate the numerical values of p and q.
Solution:

Question 8.
The ends of a diameter of a circle have the co-ordinates (3, 0) and (-5, 6). PQ is another diameter where Q has the coordinates ( -1, -2). Find the co-ordinates of P and the radius of the circle.
Solution:

Question 9.
In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B (3, -8)?
Solution:

Question 10.
Find the ratio in which the point P (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3). Hence find the value of p.
Solution:

Question 11.
In what ratio is the line joining the points (4, 2) and (3, -5) divided by the x-axis? Also, find the co-ordinates of the point of division.
Solution:

Question 12.
If the abscissa of a point P is 2, find the ratio in which it divides the line segment joining the points (-4, -3) and (6, 3). Hence, find the co-ordinates of P.
Solution:

Question 13.
Determine the ratio in which the line 2x + y – 4 = 0 divide the line segment joining the points A (2, -2) and B (3, 7). Also, find the co-ordinates of the point of division.
Solution:

Question 14.
Point A(2, -3) is reflected in the v-axis onto point A’. Then the point A’ is reflected in the line x = 4 onto the point A”.
(i) Write the coordinates of A’ and A”.
(ii) Find the ratio in which the line segment AA” is divided by the x-axis. Also, find the coordinates of the point of division.
Solution:

Question 15.
ABCD is a parallelogram. If the coordinates of A, B and D are (10, -6), (2, -6) and (4, -2) respectively, find the co-ordinates of C.
Solution:

Question 16.
ABCD is a parallelogram whose vertices A and B have co-ordinates (2, -3) and (-1, -1) respectively. If the diagonals of the parallelogram meet at the point M(1, -4), find the co-ordinates of C and D. Hence, find the perimeter of the parallelogram. find the perimeter of the parallelogram.
Solution:

Question 17.
In the adjoining figure, P (3, 1) is the point on the line segment AB such that AP : PB = 2 : 3. Find the co-ordinates of A and B.

Solution:

Question 18.
Given, O, (0, 0), P(1, 2), S(-3, 0) P divides OQ in the ratio of 2 : 3 and OPRS is a parallelogram.
Find : (i) the co-ordinates of Q.
(ii)the co-ordinates of R.
(iii) the ratio in which RQ is divided by y-axis.

Solution:

Question 19.
If A (5, -1), B (-3, -2) and C (-1, 8) are the vertices of a triangle ABC, find the length of the median through A and the co-ordinates of the centroid of triangle ABC.
Solution: