This page 10th CBSE math solution for exercise 7.1 part 4 is going to provide you solution for every problems that you find in the exercise no 7.1

(iii) (4,5) (7,6) (4,3) (1,2)

Solution:

Let the given points as A(4,5) B(7,6) C(4,3) and D (1,2)

**Distance between two points = √(x₂ - x₁)
² + (y₂ - y₁) ² **

Length of the side AB

Here x₁ = 4, y₁ = 5, x₂ = 7 and y₂ = 6

= **√(7-4)² + (6-5)² **

= **√3² + 1² **

= **√9 + 1**

= **√10**

Length of the side BC

Here x₁ = 7, y₁ = 6, x₂ = 4 and y₂ = 3

= **√(4-7)² + (3-6)² **

= **√(-3)² + (-3)² **

= **√9 + 9**

= **√18**

Length of the side CD

Here x₁ = 4, y₁ = 3, x₂ = 1 and y₂ = 2

= **√(1-4)² + (2-3)² **

= **√(-3)² + (-1)² **

= **√9 + 1**

= **√10**

Length of the side DA

Here x₁ = 1, y₁ = 2, x₂ = 4 and y₂ = 5

= **√(4-1)² + (5-2)² **

= **√3² + 3² **

= **√9 + 9**

= **√18**

**AB = CD, BC = DA. length of opposite sides are equal.**

**Length of AC**

Here x₁ = 4, y₁ = 5, x₂ = 4 and y₂ = 3

= **√(4-4)² + (3-5)² **

= **√0² + (-2)² **

= **√4**

= **2**

**Length of BD**

Here x₁ = 7, y₁ = 6, x₂ = 1 and y₂ = 2

= **√(1-7)² + (2-6)² **

= **√(-4)² + (-4)² **

= **√16 + 16 **

= **√**32

**It can be observed that opposite sides of this quadrilateral are of the same length.However, the diagonals are of different lengths.Therefore,the given points are the vertices of the parallelog**

In the page 10th CBSE math solution for exercise 7.1 part 4 we are going to see the solution of next problem

(7) Find the points on the x-axis which is equidistant from (2,-5) and (-2,9)

Solution:

We have to find the point on x-axis. So its y-coordinate will be 0.

Let the point on x axis be (x,0)

Distance between (x,0) and (2,-5) =

Distance between (x,0) and (-2,9)

**Distance between two points = √(x₂ - x₁)
² + (y₂ - y₁) ² **

Here x₁ = x, y₁ = 0, x₂ = 2 and y₂ = -5

= **√(2-x)² + (5-0)² **

= **√(2 - x)² + 25 **

Here x₁ = x, y₁ = 0, x₂ = -2 and y₂ = 9

= **√(-2-x)² + (9-0)² **

= **√(2+x)² + (9)² **

= **√****(2+x)² + 81**

**√(2 - x)² + 25 **= **√****(2+x)² + 81**

** 4 + x****² - 4 x + 25 = 4 + x****² + 4 x + 81**

** ****x****² - ****x****² - 4 x - 4 x + 4 - 4 = 81 - 25**

** -8 x = 56**

** x = -7**

**Therefore the required point is (-7,0)**

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