Given a line segment AB joining the points A (-4, 6) and B (8, -3). Find :
(ii) find the coordinates of the point of intersection. Divided by y-axis.

Answer

To find the coordinates of the point of intersection of the line segment AB with the y-axis, we can follow these steps:

### Step 1: Identify the coordinates of points A and B
The coordinates of point A are given as A(-4, 6) and point B as B(8, -3).

### Step 2: Determine the equation of the line segment AB
To find the equation of the line passing through points A and B, we first calculate the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (-4, 6) \) and \( (x_2, y_2) = (8, -3) \).

Calculating the slope:
\[ m = \frac{-3 - 6}{8 - (-4)} = \frac{-9}{12} = -\frac{3}{4} \]

### Step 3: Use the point-slope form to find the equation of the line
The point-slope form of a line is given by:
\[ y - y_1 = m(x - x_1) \]
Using point A(-4, 6):
\[ y - 6 = -\frac{3}{4}(x + 4) \]
Expanding this:
\[ y - 6 = -\frac{3}{4}x - 3 \]
\[ y = -\frac{3}{4}x + 3 \]

### Step 4: Find the intersection with the y-axis
The y-axis is defined by \( x = 0 \). To find the y-coordinate where the line intersects the y-axis, substitute \( x = 0 \) into the line equation:
\[ y = -\frac{3}{4}(0) + 3 = 3 \]

### Step 5: Write the coordinates of the intersection point
The coordinates of the point of intersection P with the y-axis are:
\[ P(0, 3) \]

### Final Answer
Thus, the coordinates of the point of intersection of the line segment AB with the y-axis are \( P(0, 3) \).

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