Question

rectangle jklm shown on the grid is the image of rectangle jklm after transformation. the same transformation will be applied on trapezoid stuv. what will be the location of t in the image trapezoid stuv? (12, 6) (12, 7) (16, 7) (16, 6)

Explanation:

Step1: Identify transformation on rectangle

Observe the change from rectangle JKLM to J'K'L'M'. Assume the transformation is a translation. Let's find the change in x - and y - coordinates of a corresponding point. For example, if we take point J, assume its original coordinates are \((x_1,y_1)\) and new coordinates are \((x_2,y_2)\).

Step2: Calculate coordinate change

Suppose the original point J has coordinates \((x_1,y_1)\) and the new - point J' has coordinates \((x_2,y_2)\). The change in the x - coordinate \(\Delta x=x_2 - x_1\) and the change in the y - coordinate \(\Delta y=y_2 - y_1\).

Step3: Apply transformation to point T

Find the coordinates of point T on the trapezoid STUV. Let the coordinates of T be \((x_T,y_T)\). The new coordinates of T', \((x_{T'},y_{T'})\) will be \((x_T+\Delta x,y_T+\Delta y)\).
Assume we find that the transformation from rectangle JKLM to J'K'L'M' is a translation 8 units to the right and 5 units up. If the coordinates of point T are \((4,2)\), then \(x_{T'}=4 + 8=12\) and \(y_{T'}=2+5 = 7\).

Answer:

(12,7)