52. Find the number of zeroes of the given figure.
(A)1
(B) 2
(0)3
(D)4
Answers
Answer:
where is figure.
Answer:
Exercise 7.1
Q.1. Find the distance between the following pairs of points:
(i) (2, 3), (4, 1) (ii) (–5, 7), (–1, 3) (iii) (a, b), (–a, –b)
Sol. (i) Here x1 = 2, y1 = 3, x2 = 4 and y2 = 1
∴ The required distance
Q.2. Find the distance between the point (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2 of the NCERT textbook?
Sol. Part-I
Let the points be P(0, 0) and Q(36, 15).
Q.3. Determine if the points (1, 5), (2, 3) and (�2, �11) are collinear.
Sol. Let the points be A(1, 5), B (2, 3) and (�2, �11)
A, B and C are collinear, if
AB + BC = AC
AC + CB = AB
But AB + BC ≠ AC
AC + CD ≠ AB
BA + AC ≠ BC
∴ A, B and C are not collinear.
Q.4. Check whether (5, –2), (6, 4) and (7, –2) are the vertices of an isosceles triangle.
Sol. Let the points be A (5, –2), B (6, 4) and (7, –2).
We have AB = BC ≠ AC
∴ΔABC is an isosceles triangle.
Q.5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. Champa and Chaneli walk into the class and after observing for a few minutes Champa asks Chaneli, “Don�t you think ABCD is a squar?” Chaneli disagrees. Using distance single formula, find which of them is correct.
Sol. Let the number of horizontal columns represent the x-coordinates whereas the vertical rows represent the y-coordinates.
∴ The points are:
A(3, 4), B(6, 7), C(9, 4) and D(6, 1)
Q.6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(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)
Sol. (i) Let the points be: A(�1, �2), B(1, 0), C(�1, 2) and D(�3, 0).
(ii) Let the points be A (�3, 5), B(3, 1), C(0, 3) and D(�1, �4).
⇒ A, B, C and D are collinear. Thus, ABCD is not a quadrilateral.
(iii) Let the points be A (4, 5), B (7, 6), C (4, 3) and D(1, 2).
Q.7. Find the point on the x-axis which is equidistant from (2, �5) and (�2, 9).
Sol. We know that any point on x-axis has its ordinate = 0.
Let the required point be P(x, 0).
Let the given points be A(2, �5) and B(�2, 9)
Q.8. Find the values of y for which the distance between the points P(2, �3) and Q(10, y) is 10 units.
Sol. The given points are P(2, �3) and Q(10, y).