Question

quadrilateral ghij is a translation of quadrilateral ghij. write the translation rule.
$(x,y)\to(x - \square,y - \quad)$

Explanation:

Step1: Identify a point and its image

Let's take point \( G(5, 2) \) and its image \( G'(-4, -5) \).

Step2: Calculate the horizontal change (\( \Delta x \))

The horizontal change is \( x' - x = -4 - 5 = -9 \). So, we subtract 9 from the \( x \)-coordinate.

Step3: Calculate the vertical change (\( \Delta y \))

The vertical change is \( y' - y = -5 - 2 = -7 \). So, we subtract 7 from the \( y \)-coordinate.
We can verify with another point, say \( J(2, 5) \) and \( J'(-7, -2) \). \( \Delta x=-7 - 2=-9 \), \( \Delta y=-2 - 5=-7 \). Similarly for \( H(7, 5) \) and \( H'(-2, -2) \): \( \Delta x=-2 - 7=-9 \), \( \Delta y=-2 - 5=-7 \).

Answer:

The translation rule is \( (x, y) \to (x - 9, y - 7) \)