Understanding the Problem
To determine the ratio in which the line joining points A(8, 9) and B(-7, 4) intersects the x-axis, we first need to find the coordinates of the intersection point. The x-axis is characterized by the condition y = 0.
Finding the Equation of the Line
- Coordinates of A: (8, 9)
- Coordinates of B: (-7, 4)
Using the two-point form of the line equation:
- Slope (m) = (y2 - y1) / (x2 - x1)
- m = (4 - 9) / (-7 - 8) = -5 / -15 = 1/3
Now, using point-slope form:
y - y1 = m(x - x1)
y - 9 = (1/3)(x - 8)
Simplifying this gives us the equation of the line.
Finding the Intersection with the X-axis
Set y = 0 in the line equation to find the x-coordinate of the intersection:
- 0 - 9 = (1/3)(x - 8)
- Solve for x to find the intersection point.
Finding the Ratio
Let the ratio be k:1.
- The coordinates of the point dividing AB in the ratio k:1 can be expressed as:
x = (k * x2 + x1) / (k + 1)
y = (k * y2 + y1) / (k + 1)
Since we need y = 0, substitute the values of A and B to find k.
Conclusion
After calculating, you will find the specific ratio k:1, which shows how the line segment is divided at the x-axis.