Understanding the Problem
To find the points on the X-axis that are at a distance of 10 units from the point A(11, -8), we need to consider the properties of distance in a coordinate plane.
Distance Formula
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
In our case, point A is (11, -8) and a point on the X-axis can be represented as (x, 0). We need to set the distance from A to this point equal to 10.
Setting Up the Equation
Using the distance formula:
√((x - 11)² + (0 + 8)²) = 10
This simplifies to:
√((x - 11)² + 64) = 10
Squaring Both Sides
To eliminate the square root, square both sides:
(x - 11)² + 64 = 100
Simplifying
Now, we can solve for x:
(x - 11)² = 36
Taking the square root:
x - 11 = ±6
This gives us two equations:
1. x - 11 = 6
2. x - 11 = -6
Finding the Points
Solving these equations:
1. x = 17
2. x = 5
So, the points on the X-axis that are 10 units away from point A(11, -8) are:
Final Points
- (17, 0)
- (5, 0)
These represent the two points on the X-axis at the specified distance from point A.