🖩 PYTHAGOREAN THEOREM (on your reference chart!): a² + b² = c² | DESMOS: Line 1: a² + b² ~ c² → Define known values → Leave unknown BLANK | c = hypotenuse (LONGEST side)
TRANSFORMATIONS: Translate: (x+a, y+b) | Reflect x-axis: (x, −y) | Reflect y-axis: (−x, y) | Rotate 90° CW: (y, −x)
Part A: Pythagorean Theorem with Desmos (Problems 1–5)
1 A TV screen at AT&T Stadium is 40 inches wide and 30 inches tall. Find the diagonal.
a = (width)
b = (height)
c = (solving for)
Line 1: a² + b² ~ c²
Line 2: a = ___
Line 3: b = ___
Line 4: c = (leave ________)
Answer: c = inches (the diagonal)
2 A ladder is 17 ft long and its base is 8 ft from a Dallas building. How high does it reach? (Find a LEG!)
a = (base)
b = (solving for: height)
c = (ladder = hypotenuse)
Line 1: a² + b² ~ c²
Line 2: a = ___
Line 3: b = (leave ________)
Line 4: c = ___
Answer: b = ft
3 Klyde Warren Park is 200 ft long and 80 ft wide. Find the diagonal path across it.
a =
b =
c = (diagonal = hypotenuse)
Line 1: a² + b² ~ c²
Line 2: a = ___
Line 3: b = ___
Line 4: c = (leave blank)
Answer: c ≈ ft
4 A ramp is 15 ft long and 9 ft high. How far is the base of the ramp from the wall?
a = (solving for: base)
b = (height)
c = (ramp = hypotenuse)
Line 1: _______________
Line 2: a = (leave ___)
Line 3: b = ___
Line 4: c = ___
Answer: a = ft
5 ⭐ A rope goes from the top of a 12 ft pole to a point on the ground 5 ft from the base. How long is the rope?
a =
b =
c = (which are you solving for?)
Type all 4 Desmos lines on your own:
Line 1: _______________
Line 2: _______________
Line 3: _______________
Line 4: _______________
Answer: = ft
Part B: Transformations (Problems 6–10)
6 Translate triangle A(1,2), B(4,2), C(1,5) → 3 units RIGHT and 2 units UP.
Rule: (x + 3, y + 2)
| Original | Rule Applied | New Point |
|---|
| A(1, 2) | (1+3, 2+2) | A'(, ) |
| B(4, 2) | (4+3, 2+2) | B'(, ) |
| C(1, 5) | (1+3, 5+2) | C'(, ) |
7 Reflect triangle A(1,2), B(4,2), C(1,5) across the y-axis.
Rule: (−x, y)
| Original | Rule Applied | New Point |
|---|
| A(1, 2) | (−1, 2) | A'(, ) |
| B(4, 2) | (, ) | B'(, ) |
| C(1, 5) | (, ) | C'(, ) |
8 Reflect point P(3, −4) across the x-axis.
Rule for x-axis: (x, −y)
P(3, −4) → P'(, )
Show work: (3, −(−4)) = (3, ___)
9 Rotate triangle D(2,1), E(5,1), F(2,4) by 90° clockwise.
Rule: (y, −x)
| Original | Rule Applied | New Point |
|---|
| D(2, 1) | (1, −2) | D'(, ) |
| E(5, 1) | (, ) | E'(, ) |
| F(2, 4) | (, ) | F'(, ) |
10 ⭐ CHALLENGE: Shape ABCD: A(1,1), B(3,1), C(3,4), D(1,4). First translate 2 RIGHT, then reflect across the x-axis.
Step 1 Rule: (x+2, y) | Step 2 Rule: (x, −y)
| Original | After Translate | After Reflect x-axis |
|---|
| A(1, 1) | (, ) | A''(, ) |
| B(3, 1) | (, ) | B''(, ) |
| C(3, 4) | (, ) | C''(, ) |
| D(1, 4) | (, ) | D''(, ) |
✅ Self-Check Before You Turn This In:
☐ Did I label a, b, c for every Pythagorean problem? (c = hypotenuse = LONGEST)
☐ Did I leave the unknown variable BLANK in Desmos?
☐ Did I write the transformation rule before applying it?
☐ Did I apply the rule to EVERY point (not just one)?