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

Question 7

Step 1: First, write down the vertices of the triangle.

\(A(3,0),\ B(7,0),\ C(8,4)\).

Step 2: Find the base.

The base is the distance between points \(A(3,0)\) and \(B(7,0)\).

Since both points are on the x-axis (y = 0), the distance is simply:

\(AB = 7 - 3 = 4\, \text{units}\).

Step 3: Find the height.

The height is the perpendicular distance from point \(C(8,4)\) to the x-axis.

The y-coordinate of point C is 4, so the height is:

\(h = 4\, \text{units}\).

Step 4: Use the area formula for a triangle.

\( \text{Area} = \dfrac{1}{2} \times \text{base} \times \text{height} \)

Step 5: Substitute the values.

\( \text{Area} = \dfrac{1}{2} \times 4 \times 4 = 8 \)

Final Answer: The area of the triangle is \(8\, \text{square units}\).