Draw triangle ABC with vertices A(4,2), B(1,2) and C(1,4) using a scale of 1cm to represent I unit on each axis. Draw Triangle A’B’C’ under the reflection in the line y = 1, then triangle A’’B’’C’’ under a reflection in the line x = 0.
To draw Triangle ABC with the given vertices A(4,2), B(1,2), and C(1,4) using a scale of 1cm to represent 1 unit on each axis, follow these steps:
1. Draw the x and y axes on a sheet of graph paper.
2. Locate the point A(4,2) on the graph paper. Starting from the origin, move 4 units to the right along the x-axis and 2 units upwards along the y-axis. Mark this point as A.
3. Locate the point B(1,2) on the graph paper. Starting from the origin, move 1 unit to the right along the x-axis and 2 units upwards along the y-axis. Mark this point as B.
4. Locate the point C(1,4) on the graph paper. Starting from the origin, move 1 unit to the right along the x-axis and 4 units upwards along the y-axis. Mark this point as C.
5. Connect the points A, B, and C to form Triangle ABC.
To draw the reflection of Triangle ABC in the line y = 1 (Triangle A'B'C'), follow these additional steps:
1. Draw the line y = 1 on the graph paper.
2. Reflect each vertex of Triangle ABC across the line y = 1 to find the corresponding vertices of Triangle A'B'C'.
- Vertex A(4,2) is reflected as A'(4,0).
- Vertex B(1,2) is reflected as B'(1,0).
- Vertex C(1,4) is reflected as C'(1,2).
3. Connect the points A', B', and C' to form Triangle A'B'C'.
To draw the reflection of Triangle A'B'C' in the line x = 0 (Triangle A''B''C''), follow these additional steps:
1. Draw the line x = 0 on the graph paper.
2. Reflect each vertex of Triangle A'B'C' across the line x = 0 to find the corresponding vertices of Triangle A''B''C''.
- Vertex A'(4,0) is reflected as A''(-4,0).
- Vertex B'(1,0) is reflected as B''(-1,0).
- Vertex C'(1,2) is reflected as C''(-1,2).
3. Connect the points A'', B'', and C'' to form Triangle A''B''C''.
Remember to label the vertices of all the triangles for clarity.
To draw triangle ABC with the given vertices A(4,2), B(1,2), and C(1,4) using a scale of 1cm to represent 1 unit on each axis, follow these steps:
1. Start by drawing the x-axis and the y-axis on your graph paper. Make sure to label the axes accordingly.
2. Determine the scale you will use to represent the units on each axis. In this case, we have a scale of 1 cm = 1 unit.
3. Plot point A(4,2) on the graph by measuring 4 units to the right on the x-axis and 2 units up on the y-axis from the origin (intersection of x-axis and y-axis). Mark this point with a dot or a small circle.
4. Similarly, plot point B(1,2) by measuring 1 unit to the right on the x-axis and 2 units up on the y-axis from the origin. Mark this point on the graph.
5. Plot point C(1,4) by measuring 1 unit to the right on the x-axis and 4 units up on the y-axis. Mark this point on the graph.
6. Connect the dots A, B, and C with straight lines to form triangle ABC.
To find the reflection of triangle ABC in the line y = 1, follow these steps:
1. Draw the line y = 1 on your graph paper. This line is a horizontal line passing through the y-coordinate 1.
2. Reflect each vertex of triangle ABC across the line y = 1 to find the corresponding vertices of triangle A'B'C'.
- To reflect a point across a horizontal line, find the same distance above or below the line and plot the reflected point.
- For example, point A (4, 2) will reflect to A' (4, 0) since it is 2 units below the line y = 1.
- Similarly, point B (1, 2) will reflect to B' (1, 0) and point C (1, 4) will reflect to C' (1, 6).
3. Connect the new vertices A', B', and C' to form triangle A'B'C'. This new triangle will be the reflection of triangle ABC in the line y = 1.
To find the reflection of triangle A'B'C' in the line x = 0, follow these steps:
1. Draw the line x = 0 on your graph paper. This line is a vertical line passing through the x-coordinate 0.
2. Reflect each vertex of triangle A'B'C' across the line x = 0 to find the corresponding vertices of triangle A''B''C''.
- To reflect a point across a vertical line, find the same distance to the left or right of the line and plot the reflected point.
- For example, point A' (4, 0) will reflect to A'' (-4, 0) since it is 4 units to the left of the line x = 0.
- Similarly, point B' (1, 0) will reflect to B'' (-1, 0) and point C' (1, 6) will reflect to C'' (-1, 6).
3. Connect the new vertices A'', B'', and C'' to form triangle A''B''C''. This new triangle will be the reflection of triangle A'B'C' in the line x = 0.
Now, you have successfully drawn triangle ABC, as well as its reflections A'B'C' and A''B''C'' in the lines y = 1 and x = 0.
to reflect across y=1, (x,y) → (x,2-y)
across x=0 (the y-axis), (x,y) → (-x,y)
so make the needed adjustments.
Of course, if you're just doing the drawing as requested, simply flip your ruler across the indicated line. That's easy enough if you're using graph paper.