Parallelogram JKLM is reflected across the y-axis and then translated down 6 units to form parallelogram QRST.
reverse all the x-coordinates, then
subtract 6 from all the y-coordinates
To understand how the reflection and translation affect the parallelogram JKLM to form parallelogram QRST, let's break it down step by step.
Step 1: Reflection across the y-axis
Reflecting a shape across the y-axis means that each point of the original shape gets mirrored or "flipped" to the opposite side of the y-axis while maintaining the same distance from the y-axis.
So, to reflect parallelogram JKLM across the y-axis:
1. Identify each vertex of JKLM: J, K, L, M.
2. For each vertex, switch the x-coordinate sign while keeping the y-coordinate the same.
For example, if J = (3, 2), after reflection across the y-axis, it becomes J' = (-3, 2).
Step 2: Translation downward 6 units
A translation involves moving a shape in a particular direction without changing its orientation or shape. In this case, we are translating the reflected parallelogram JKLM to form parallelogram QRST by moving it downward 6 units.
To translate the reflected parallelogram JKLM downward 6 units:
1. For each reflected vertex (J', K', L', M'), subtract 6 from the y-coordinate to move it down.
For example, if J' = (-3, 2), after the translation, it becomes Q = (-3, 2 - 6) = (-3, -4).
Repeat the same process for each reflected vertex to get the coordinates of the corresponding vertices of parallelogram QRST: Q, R, S, and T.
Finally, you can define parallelogram QRST using the coordinates of its vertices Q, R, S, and T, which are obtained after reflecting parallelogram JKLM across the y-axis and translating it downward 6 units.