`{:("Quantity A","Quantity B"),("The distance between points","The distance between points"),("(0,9) and (-2,0)","(3, 9) and (10, 3)"):}`

Answer

To solve the problem, we need to calculate the distances for both Quantity A and Quantity B using the distance formula. The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step 1: Calculate the distance for Quantity A
The points given for Quantity A are \((0, 9)\) and \((-2, 0)\).

1. Identify the coordinates:
- \(x_1 = 0\), \(y_1 = 9\)
- \(x_2 = -2\), \(y_2 = 0\)

2. Substitute the values into the distance formula:
\[ d_A = \sqrt{((-2) - 0)^2 + (0 - 9)^2} \]

3. Simplify the expression:
\[ d_A = \sqrt{(-2)^2 + (-9)^2} = \sqrt{4 + 81} = \sqrt{85} \]

### Step 2: Calculate the distance for Quantity B
The points given for Quantity B are \((3, 9)\) and \((10, 3)\).

1. Identify the coordinates:
- \(x_1 = 3\), \(y_1 = 9\)
- \(x_2 = 10\), \(y_2 = 3\)

2. Substitute the values into the distance formula:
\[ d_B = \sqrt{(10 - 3)^2 + (3 - 9)^2} \]

3. Simplify the expression:
\[ d_B = \sqrt{(7)^2 + (-6)^2} = \sqrt{49 + 36} = \sqrt{85} \]

### Step 3: Compare the distances
Now that we have calculated both distances:
- Quantity A: \(d_A = \sqrt{85}\)
- Quantity B: \(d_B = \sqrt{85}\)

Since both distances are equal, we conclude that:

**Final Answer:** The two quantities are equal.