Ram is walking along the line joining (1, 4) and (0, 6)
Rahim is walking along the line Joining (3, 4) and (1, 0)
Represent on graph and find the point where both of them cross each other

Answer

To solve the problem step-by-step, we will find the equations of the lines along which Ram and Rahim are walking, plot these lines on a graph, and then determine the point where they intersect.

### Step 1: Find the equation of Ram's line
Ram is walking along the line joining the points (1, 4) and (0, 6).

1. **Calculate the slope (m)** of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 4}{0 - 1} = \frac{2}{-1} = -2 \]

2. **Use the point-slope form** of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
Using point (1, 4):
\[ y - 4 = -2(x - 1) \]
Simplifying:
\[ y - 4 = -2x + 2 \implies y = -2x + 6 \]

### Step 2: Find the equation of Rahim's line
Rahim is walking along the line joining the points (3, 4) and (1, 0).

1. **Calculate the slope (m)** of the line:
\[ m = \frac{0 - 4}{1 - 3} = \frac{-4}{-2} = 2 \]

2. **Use the point-slope form** of the equation of a line:
Using point (3, 4):
\[ y - 4 = 2(x - 3) \]
Simplifying:
\[ y - 4 = 2x - 6 \implies y = 2x - 2 \]

### Step 3: Find the intersection point
To find the point where both lines intersect, we need to solve the equations:
1. \(y = -2x + 6\)
2. \(y = 2x - 2\)

Set the equations equal to each other:
\[ -2x + 6 = 2x - 2 \]
Combine like terms:
\[ 6 + 2 = 2x + 2x \implies 8 = 4x \implies x = 2 \]

Now substitute \(x = 2\) back into one of the equations to find \(y\):
Using \(y = -2x + 6\):
\[ y = -2(2) + 6 = -4 + 6 = 2 \]

Thus, the intersection point is \((2, 2)\).

### Step 4: Graph the lines
1. Plot the points (1, 4) and (0, 6) for Ram's line and draw the line through these points.
2. Plot the points (3, 4) and (1, 0) for Rahim's line and draw the line through these points.
3. Mark the intersection point (2, 2) on the graph.

### Final Answer
The point where Ram and Rahim cross each other is \((2, 2)\).

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