Question

the table below gives the coordinates of a figure that was translated. which of the following statements is not true?

x (-4, 9)	x (3, 7)
y (-6, 4)	y (1, 2)
z (-3, 4)	z (4, 2)

the pre - image was in located in quadrant iii.
the figure was translated 7 units right and 2 units down.
the translation can be represented by (x + 7,y - 2).
all the above are true.

Explanation:

Step1: Analyze quadrant of pre - image

The pre - image points are \(X(-4,9)\), \(Y(-6,4)\), \(Z(-3,4)\). Points with \(x<0\) and \(y > 0\) are in Quadrant II, not Quadrant III.

Step2: Analyze translation rule

For \(X(-4,9)\) to \(X'(3,7)\): \(x\) changes from \(- 4\) to \(3\) (\(-4 + 7=3\)) and \(y\) changes from \(9\) to \(7\) (\(9-2 = 7\)). Similarly for \(Y\) and \(Z\), the translation is 7 units right (\(x+7\)) and 2 units down (\(y - 2\)).

Answer:

A. The pre - image was in located in Quadrant III.