If the distance between the points (6, 0) and (0, y) is 10 units, find the value of y.

Answer

To solve the problem of finding the value of \( y \) given the distance between the points \( (6, 0) \) and \( (0, y) \) is 10 units, we can follow these steps:

### Step 1: Identify the points
We have two points:
- Point A: \( (6, 0) \)
- Point B: \( (0, y) \)

### Step 2: Use the distance formula
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In our case, we can assign:
- \( (x_1, y_1) = (6, 0) \)
- \( (x_2, y_2) = (0, y) \)

### Step 3: Substitute the points into the distance formula
Substituting the coordinates into the distance formula, we have:
\[ 10 = \sqrt{(0 - 6)^2 + (y - 0)^2} \]

### Step 4: Simplify the equation
This simplifies to:
\[ 10 = \sqrt{(-6)^2 + y^2} \]
\[ 10 = \sqrt{36 + y^2} \]

### Step 5: Square both sides to eliminate the square root
Squaring both sides gives:
\[ 10^2 = 36 + y^2 \]
\[ 100 = 36 + y^2 \]

### Step 6: Solve for \( y^2 \)
Now, we can isolate \( y^2 \):
\[ y^2 = 100 - 36 \]
\[ y^2 = 64 \]

### Step 7: Take the square root
Taking the square root of both sides gives:
\[ y = \sqrt{64} \]
\[ y = 8 \quad \text{or} \quad y = -8 \]

### Conclusion
Thus, the possible values for \( y \) are \( 8 \) and \( -8 \).

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