Using x = 3 and y = 4 — same numbers, different order — different answers:
✗ Wrong Order
x = 3 y = 4
↓ add first ← ERROR
3 + 4 = 7
↓ then square
7² = 49
↓ root
√49 = 7 ✗
✓ Right Order
↓ square each first
x=3 3²=9
y=4 4²=16
↓ then add
9 + 16 = 25
↓ root
√25 = 5 ✓
Worked Example — Watch Each Step
Distance from A = (1, 1) to B = (4, 5)
The Right Triangle — A(1,1) to B(4,5)
Square 3 and 4 separately → add → square root = 5
Hover (or tap) each step — it lights up in the diagram above
1
Write the two points. A = (1, 1) · B = (4, 5)
2
Subtract x-values: 4 − 1 = 3 Square it: 3² = 9
3
Subtract y-values: 5 − 1 = 4 Square it: 4² = 16
4
Add both squared results: 9 + 16 = 25
5
Square root: √25 = 5 Distance = 5 grid units ✅
Today's Fixed Points — These Never Change
A
(4, 2)
Tip-off — always
B
( ? , ? )
You pick this next
G
(8, 2)
Opponent's goal
B is where the ball landed after your bot's best charge in Season 1. You will place it on the grid in the next section.
Mark the Field
Tap the grid to place Point B — where did the ball land?
The 8 × 4 Field — Tap to Place Point B
Think back to Season 1. After your bot's best charge — which grid square did the ball end up in? Tap that square. B is your estimate — it does not need to be perfect. The math works either way.
A = Tip-off (4,2)
G = Opponent Goal (8,2)
B = Your Ball Position (tap to place)
A
(4, 2)
Tip-off · fixed
B
Tap grid ↑
Your ball position
G
(8, 2)
Opponent goal · fixed
✅ Point B Placed
You placed B at . You can tap a different square to move it. When you're happy, continue below.
👆 Tap the Grid Above
Tap anywhere on the field to place Point B. Choose the square closest to where the ball actually landed.
Three Calculations
Fill in each blank. The formula guides you step by step.
Rule: Square each part separately — then add
x = 3
3² = 9
+
y = 4
4² = 16
9+16=25
√25 = 5 ✓
1
Distance A → G (Tip-off to Opponent's Goal)
A = (4, 2) → G = (8, 2)Both given — just follow the steps.
Check Step 2: 8 − 4 = 4, then 4² = 16. Check Step 3: 2 − 2 = 0, then 0² = 0. Step 4: 16 + 0 = 16. Step 5: √16 = 4. The answer for A→G is always exactly 4 grid units.
✅ A→G = 4 grid units. The ball needs to travel 4 units to reach the goal from tip-off.
2
Distance B → G (Your Ball to the Goal)
B = (?, ?) → G = (8, 2)
Step 2 — x values:x₂ − x₁ = 8 − ? = → squared:
Step 3 — y values:y₂ − y₁ = 2 − ? = → squared:
Step 4 — add: + =
Step 5 — √ :d = √ ≈ grid units
💡 Hint for B → G
Follow the same steps as A→G. Use your B coordinates from the grid. For Step 5, use your calculator's √ button and round to the nearest whole number.
3
Distance A → B (How Far Did the Charge Move the Ball?)
A = (4, 2) → B = (?, ?)
Step 2 — x values:x₂ − x₁ = ? − 4 = → squared:
Step 3 — y values:y₂ − y₁ = ? − 2 = → squared:
Step 4 — add: + =
Step 5 — √ :d = √ ≈ grid units
💡 Hint for A → B
A is always (4,2). B is your placed coordinate. Subtract: B_x − 4 for x, B_y − 2 for y. Square each. Add. Take the square root.
Compare + Reflect
See your three distances — then answer four questions
Your Field + Three Points
A reminder of what you marked: A = tip-off (4, 2), B = your ball position, G = goal (8, 2).
A
(4, 2)
Tip-off
B
—
Your ball
G
(8, 2)
Goal
Your Three Distances
A → G
—
A → B
—
B → G
—
Distance
Your Formula Result
Grid Count Check
A → G (tip-off to goal)
—
A → B (charge distance)
—
B → G (remaining to goal)
—
📏 Grid Count Check: Walk to the field. For each pair of points, trace the straight line between them and count the grid squares that line runs along — count straight across for a flat line, or corner-to-corner through the squares for a slanted one. Write those counts in the table above. If your count is more than 1 off from the formula, check Step 2 of that calculation.
Reflect — Answer as a Team
Question 1
How much of the full A→G distance did your charge close? Write it as a fraction and a percent.
A→G = ? units · A→B = ? units Fraction: A→B ÷ A→G = _____ · Percent: _____ %
💡 How do I write it as a fraction?
Divide: A→B ÷ A→G. Example: if A→B = 2 and A→G = 4, the fraction is 2/4 = 1/2 = 50%. Your charge closed half the distance.
Your charge moved the ball units. That is out of 4 total units, which is %.
Question 2
How many straight-line charges like this would theoretically be needed to score from tip-off?
Divide A→G by A→B. Round up to the nearest whole number. Example: If A→G = 4 and A→B = 2, you need 4 ÷ 2 = 2 charges (minimum).
💡 What if I get 1?
Getting 1 means your charge is long enough to score in one shot — theoretically. Did that actually happen in your match? If not, think about why: the path may not be perfectly straight, or contact may have been off-center.
A→G ÷ A→B = ÷ ≈ . So you would need about charges to score.
Question 3
The formula gives a straight-line distance. Why might your calculated A→B be different from where the ball actually ended up?
💡 Think about what happened during the charge
Your B is an estimate from memory — not an exact measurement. Also think about: did the scoop hit the ball in the center? Did the ball roll straight, or curve? A straight-line formula can't account for roll or off-center contact.
Question 4 — Season 2 Decision
Name one stat you would change for Season 2 to close more distance in a single charge. What is the tradeoff?
Power controls charge speed and follow-through distance.
Increasing Power costs points from another stat. Name the stat you'd increase, the stat you'd reduce, and why that tradeoff makes sense.
💡 I'm not sure what to reduce
Look at your Season 1 stat card. Which stats did you put the most points into? If you increase Power by 2, you need to take 2 points from somewhere. Ask: which stat matters less for closing distance — Speed, Endurance, or Turning?
Calculations Complete!
You used the distance formula three times, compared formula results to real-world distances, and named a Season 2 stat decision. Your Q4 answer goes into your reallocation next week.