Question

1. which of the following is not true about the translation shown in the graph?

a) the image and pre-image
have the same orientation.
b) the transformation preserved
the congruence of the object
c) the object moved from
quadrant iv to quadrant i
d) the translation can be described by
(x, y) \
ightarrow (x, y - 7).

Explanation:

To solve this, we analyze each option based on translation properties:

Option a:

Translation preserves orientation (same direction of vertices). So image and pre - image have same orientation. This is true.

Option b:

Translation is a rigid transformation, so it preserves congruence (shape and size). This is true.

Option c:

Pre - image (A, B, C, O) is in Quadrant I (x>0, y>0). Image (A', B', C', D) is in Quadrant IV? No, wait—wait, pre - image: Let's check coordinates. If pre - image is above the x - axis (Quadrant I) and image is below? Wait, no—wait, the pre - image (A, B, C, O) is in Quadrant I (positive x and positive y). The image (A', B', C', D) is in Quadrant IV? No, Quadrant IV is x>0, y<0. Wait, no—wait, the original figure (pre - image) is in Quadrant I (since y - coordinates are positive). The image is below, so y - coordinates are negative? Wait, no, the option says "moved from Quadrant IV to Quadrant I"—but pre - image is in Quadrant I, image in Quadrant IV? Wait, no, the statement c says "The object moved from quadrant IV to quadrant I"—but the pre - image (original) is in Quadrant I (since points like A, B have positive y), and image is in Quadrant IV? No, that's reversed. Wait, no—wait, maybe I misread. Wait, the pre - image: Let's see the graph. The pre - image (A, B, C, O) is in Quadrant I (x positive, y positive). The image (A', B', C', D) is in Quadrant IV? No, Quadrant IV is x positive, y negative. Wait, the statement c says the object moved from Quadrant IV to Quadrant I—but the pre - image is in Quadrant I, image in Quadrant IV. So the movement is from Quadrant I to Quadrant IV, not IV to I. So statement c is false? Wait, no, let's check other options.

Option d:

To check the translation rule: Let's take a point, say A. Suppose A has coordinates (x, y), and A' has coordinates (x, y - 7) (since moving down 7 units). So if A is at (let's say) (2, 6), A' would be (2, 6 - 7)=(2, - 1), which matches the graph (moving down 7 units). So the translation rule (x, y)→(x, y - 7) is correct. So d is true.

Wait, but let's re - examine option c: The "object" (pre - image) is in Quadrant I (since y - coordinates are positive). The image is in Quadrant IV (y - coordinates negative, x positive). So the object did NOT move from Quadrant IV to Quadrant I (it moved from I to IV). So option c is NOT true. Wait, but let's confirm:

• Translation preserves orientation (a: true).
• Translation preserves congruence (b: true).
• The pre - image is in Quadrant I (x>0, y>0), image in Quadrant IV (x>0, y<0). So moving from I to IV, not IV to I. So c is false.
• Translation down 7: (x, y)→(x, y - 7) (d: true).

So the answer is option c.

Answer:

c) The object moved from quadrant IV to quadrant I