NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 7: Coordinate Geometry - Exercise 7.1

Question 8

Step 1: Recall the distance formula

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Step 2: Find the distance between \((-4,0)\) and \((0,3)\)

\[ d_1 = \sqrt{(0 - (-4))^2 + (3 - 0)^2} = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \]

Step 3: Find the distance between \((4,0)\) and \((0,3)\)

\[ d_2 = \sqrt{(0 - 4)^2 + (3 - 0)^2} = \sqrt{(-4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \]

Step 4: Find the distance between \((-4,0)\) and \((4,0)\)

\[ d_3 = \sqrt{(4 - (-4))^2 + (0 - 0)^2} = \sqrt{(8)^2 + 0} = \sqrt{64} = 8 \]

Step 5: Compare the sides

We have: \(d_1 = 5\), \(d_2 = 5\), \(d_3 = 8\).

Two sides are equal (\(5\) and \(5\)).

Final Answer: A triangle with two equal sides is an isosceles triangle.