Review Sheet for the Unit 1 Assessment
Twelve questions in the same format and order as the assessment: right triangles, distance, word problems with a required sketch, translations by vector, and reflections across all four lines.
Directions
Before you start
- Show all work. An answer with no supporting equation earns no credit on the assessment.
- Round every answer to two decimal places unless the answer is exact.
- Questions 5 and 6 require a labeled sketch before any algebra.
- For every transformation question, state the coordinates of the corner points of the new image.
- Attempt all twelve questions before opening a single solution. Give yourself about 40 minutes.
- Each question group has a Khan Academy video attached. Use it only after you have tried the questions — and note that the videos do not appear on the printed copy.
Formulas provided
Transformation rules are not provided on the assessment. Know them.
Questions 1 & 2 — Solve for the identified variable
Round each answer to two decimal places.
Solve for \(x\).
Show solution
The 15 is the hypotenuse, so this is a subtraction problem.
Solve for \(y\).
Show solution
Both legs are known, so the two squares are added.
Questions 3 & 4 — Find the distance between the two points
Either method is acceptable: build a right triangle on the grid, or read the coordinates and use the distance formula.
Find the distance between the two plotted points.
Show solution
The points are \((-4,3)\) and \((2,-5)\). The horizontal leg is 6 units and the vertical leg is 8 units.
This is a 6–8–10 triangle, a multiple of the 3–4–5 triple.
Find the distance between the two plotted points.
Show solution
The points are \((-6,-2)\) and \((3,4)\).
Questions 5 & 6 — Draw a picture, then solve
A labeled sketch is worth points on its own. Draw the right angle, label the two known measurements, and mark the unknown before substituting.
The ladder
A 15-foot ladder is leaned against a building so that the top of the ladder reaches exactly 12 feet up the building. How far from the base of the building is the base of the ladder?
Show solution
The ladder is the hypotenuse. The building is the vertical leg and the ground is the horizontal leg.
The base of the ladder sits 9 feet from the building — a 9–12–15 triangle.
The rectangle
What is the length of a diagonal of a rectangle whose width is 22 inches and length is 36 inches?
Show solution
A diagonal cuts the rectangle into two right triangles. The width and length are the legs; the diagonal is the hypotenuse.
Questions 7 & 8 — Translations
Sketch the translation of the figure by the given vector, then state the coordinates of the corner points of the new image.
Translate by the vector \([4,\,-2]\).
Show solution
The rule is \((x,y)\rightarrow(x+4,\;y-2)\): right 4 units, down 2 units.
| Preimage | Image |
|---|---|
| A(−6, 2) | A′(−2, 0) |
| B(−2, 5) | B′(2, 3) |
| C(−1, 1) | C′(3, −1) |
Translate by the vector \([-3,\,-5]\).
Show solution
The rule is \((x,y)\rightarrow(x-3,\;y-5)\): left 3 units, down 5 units.
| Preimage | Image |
|---|---|
| S(2, 3) | S′(−1, −2) |
| T(6, 3) | T′(3, −2) |
| U(6, 7) | U′(3, 2) |
| V(2, 7) | V′(−1, 2) |
Questions 9 – 12 — Reflections
Sketch the reflection of the image over the given line, then state the coordinates of the corner points of the new image.
Reflect over the x-axis.
Show solution
Rule: \((x,y)\rightarrow(x,-y)\). Each y-coordinate changes sign.
\(A(-7,6)\rightarrow A'(-7,-6)\), \(B(-3,8)\rightarrow B'(-3,-8)\), \(C(-2,3)\rightarrow C'(-2,-3)\).
Reflect over the line \(y=-x\).
Show solution
Rule: \((x,y)\rightarrow(-y,-x)\). The coordinates switch places and both change sign.
\(A(2,6)\rightarrow A'(-6,-2)\) and \(B(7,3)\rightarrow B'(-3,-7)\).
Reflect over the y-axis.
Show solution
Rule: \((x,y)\rightarrow(-x,y)\). Each x-coordinate changes sign.
\(A(3,2)\rightarrow A'(-3,2)\), \(B(8,2)\rightarrow B'(-8,2)\), \(C(6,7)\rightarrow C'(-6,7)\), \(D(2,6)\rightarrow D'(-2,6)\).
Reflect over the line \(y=x\).
Show solution
Rule: \((x,y)\rightarrow(y,x)\). The coordinates switch places.
\(A(-5,-1)\rightarrow A'(-1,-5)\), \(B(-1,-3)\rightarrow B'(-3,-1)\), \(C(-2,-7)\rightarrow C'(-7,-2)\).
Answer Key & Reteach Guide
Check answers only after attempting all twelve. The last column names the lesson to revisit for any question that was missed.
| # | Answer | Skill | Revisit |
|---|---|---|---|
| 1 | \(x\approx 13.27\) | Solving for a leg | Lesson 1 |
| 2 | \(y\approx 13.60\) | Solving for the hypotenuse | Lesson 1 |
| 3 | 10.00 units | Distance from a graph | Lesson 1 Day 2 |
| 4 | \(\approx 10.82\) units | Distance from a graph | Lesson 1 Day 2 |
| 5 | 9.00 feet | Application with sketch | Lesson 1 Day 3 |
| 6 | \(\approx 42.19\) inches | Application with sketch | Lesson 1 Day 3 |
| 7 | A′(−2, 0), B′(2, 3), C′(3, −1) | Translation by vector | Lesson 3 |
| 8 | S′(−1, −2), T′(3, −2), U′(3, 2), V′(−1, 2) | Translation by vector | Lesson 3 |
| 9 | A′(−7, −6), B′(−3, −8), C′(−2, −3) | Reflection across the x-axis | Lesson 4 Day 1 |
| 10 | A′(−6, −2), B′(−3, −7) | Reflection across \(y=-x\) | Lesson 4 Day 2 |
| 11 | A′(−3, 2), B′(−8, 2), C′(−6, 7), D′(−2, 6) | Reflection across the y-axis | Lesson 4 Day 1 |
| 12 | A′(−1, −5), B′(−3, −1), C′(−7, −2) | Reflection across \(y=x\) | Lesson 4 Day 2 |