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The figure shows triangle PQR and some of its transformed images on a coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle labeled PQR is shown on ordered pair 1, 1 and 1, 4 and 3, 1. Another triangle labeled image A is shown on ordered pair 1, negative 1 and 1, negative 4 and 3, negative 1. Another triangle labeled image B is shown on ordered pair negative1, negative 1 and negative 1, negative 4 and negative 3, negative 1. Another triangle labeled image C is shown on ordered pair negative 5, 1 and negative 5, 4 and negative 3, 1. Another triangle labeled image D is shown on ordered pair negative1, 1 and negative 1, 4 and negative 3, 1. Which of the four triangles was formed by a translation of triangle PQR? A B C D

Respuesta :

sqdancefan

Answer:

C

Step-by-step explanation:

Triangle A is a reflection across the x-axis. All the y coordinates are negated.

Triangle B is a rotation 180° about the origin. All coordinates are negated.

Triangle C is a translation to the left by 6 units. 6 is subtracted from each x-coordinate.

Triangle D is a reflection across the y-axis. All the x-coordinates are negated.

_____

Comment on presentation

Your question would be much easier to read if you would simply use minus signs (hyphens) and conventional ordered-pair presentation: (1, -1), (1, -4), (3, -1), for example, for triangle A.

Answer with explanation:

Coordinates of Vertices of Δ PQR =P(1,1),Q(1,4) and R(3,1)

The Coordinates of Vertices of Triangle after Translation are

1.⇒ P'(1,-1),Q'(1,-4), R'(3,-1)---------A

2.⇒ P'(-1,-1),Q'(-1,-4), R'(-3,-1)---------B

3.⇒P'(-5,1),Q'(-5,4) ,R'(-3,1)..............C

4.⇒P'(-1,1),Q'(-1,4), R'(-3,1)---------D

There are four kind of transformations.⇒1. Rotation.2→Reflection.3→Translation .4→Dilation

⇒Image A is obtained by reflecting the Pre image along Positive X axis.

⇒≡Image B is obtained by Rotating the preimage either in Anticlockwise or Clockwise direction by angle of 180°.

⇒≡Image D is obtained by reflecting the Pre image along Positive Y axis.

⇒⇒≡Image C is obtained by translating the Pre image Horizontally 6 units left.

⇒P(1,1)=P'(1-6,1)=P'(-5,1)

⇒Q(1,4)=Q'(1-6,4)=Q'(-5,4)

⇒R(3,1)=R'(3-6,1)=R'(-3,1)

Option 3, is Correct translation of ΔPQR.

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