Write the name of the figure formed by joining the points A (-3, 0), B (0, 3) and C (3, 0) in the cartesian plane.

Answer

To determine the name of the figure formed by joining the points A (-3, 0), B (0, 3), and C (3, 0) in the Cartesian plane, we can follow these steps:

### Step 1: Plot the Points
First, we need to plot the given points on the Cartesian plane.

- Point A (-3, 0): This point has a negative x-coordinate and a y-coordinate of 0, so it lies on the negative x-axis.
- Point B (0, 3): This point has an x-coordinate of 0 and a positive y-coordinate, so it lies on the positive y-axis.
- Point C (3, 0): This point has a positive x-coordinate and a y-coordinate of 0, so it lies on the positive x-axis.

### Step 2: Connect the Points
Next, we connect the points A, B, and C.

- Draw a line segment from A to B.
- Draw a line segment from B to C.
- Draw a line segment from C to A.

### Step 3: Analyze the Shape
Now, we need to analyze the shape formed by these points.

- The distance between points A and B, B and C, and C and A needs to be calculated to determine the type of triangle formed.
- The lengths of the sides can be calculated using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step 4: Calculate the Lengths of the Sides
1. **Length AB**:
\[ AB = \sqrt{(0 - (-3))^2 + (3 - 0)^2} = \sqrt{(3)^2 + (3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \]

2. **Length BC**:
\[ BC = \sqrt{(3 - 0)^2 + (0 - 3)^2} = \sqrt{(3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \]

3. **Length CA**:
\[ CA = \sqrt{(-3 - 3)^2 + (0 - 0)^2} = \sqrt{(-6)^2 + 0} = \sqrt{36} = 6 \]

### Step 5: Determine the Type of Triangle
- We see that lengths AB and BC are equal (both are \(3\sqrt{2}\)), while CA is different (6).
- Since two sides are equal, the triangle formed is an **isosceles triangle**.

### Final Answer
The figure formed by joining the points A (-3, 0), B (0, 3), and C (3, 0) is an **isosceles triangle**.

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