Please use this for the portfolio. You will need graph paper.
1. Start with Triangle ABC with vertices: A(0,2), B(2,5), C(3,0)
2. Find slope of side AB and BC
3. Now TRANSLATE the Triangle 4 units left, and 2 units up (x-4,y+2) and give the new vertices to find A', B', C'
4. Find the slope of AB' and BC' .....(the slope of AB and BC AFTER the Translation above).
5. Now take the Triangle from #3 and REFLECT it over the X-axis and give the new vertices of A", B", C".
6. Find the slope of AB" and BC"....(the slope of AB and BC after the reflection above)
2. m AB = (5-2)/(2-0) = 3/2.
m BC = (0-5)/(3-2) = -5/1 = -5.
3. A'(-4,4), B'(-2,7), C'(1,2).
4. m AB' = (7-4)/(-2+4) = 3/2.
m BC' = (2-7)/(1+2) = -5/3
To solve this question and complete the portfolio task, follow these steps:
1. Start with Triangle ABC with vertices: A(0,2), B(2,5), C(3,0).
- Draw Triangle ABC on the graph paper with the given coordinates.
2. Find the slope of side AB and BC.
- Use the slope formula: slope = (change in y) / (change in x).
- For AB: slope_AB = (5 - 2) / (2 - 0) = 3 / 2.
- For BC: slope_BC = (0 - 5) / (3 - 2) = -5.
3. Now, TRANSLATE the Triangle 4 units left and 2 units up (x-4, y+2) to find the new vertices A', B', C'.
- To apply the translation, subtract 4 from the x-coordinates and add 2 to the y-coordinates.
- For A': A'(0-4, 2+2) = A'(-4, 4).
- For B': B'(2-4, 5+2) = B'(-2, 7).
- For C': C'(3-4, 0+2) = C'(-1, 2).
4. Find the slope of AB' and BC' (the slope of AB and BC AFTER the translation above).
- Use the slope formula.
- For AB': slope_AB' = (7 - 4) / (-2 - (-4)) = 3 / 2.
- For BC': slope_BC' = (2 - 7) / (-1 - (-2)) = -5.
5. Now, take the Triangle from Step 3 and REFLECT it over the X-axis to find the new vertices A", B", C".
- To reflect over the X-axis, negate the y-coordinates.
- For A": A"(-4, -4).
- For B": B"(-2, -7).
- For C": C"(-1, -2).
6. Find the slope of AB" and BC" (the slope of AB and BC after the reflection above).
- Use the slope formula.
- For AB": slope_AB" = (-7 - (-4)) / (-2 - (-4)) = -3 / 2.
- For BC": slope_BC" = (-2 - (-7)) / (-1 - (-2)) = 5.
Congratulations! You have completed the steps for finding the slopes of the triangle after translation and reflection. Make sure to include all the steps and answers in your portfolio.