Respuesta :
The correct options about the dilation are; Options A, B and E
How to interpret Dilated Objects?
From the given information, find attached a dilated image.
The scale factor is 2
QRS → Q'R'S' = (x,y) → 2(x,y)
The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)
To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.
2(x, y) = (2x, 2y)
The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)
To determine the statements that are true about the image ΔQ'R'S,
Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.
A) DO, 2 (x, y) = (2x, 2y)
A dilation about the origin with a scale factor 2 is described using the above notation.
Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)
R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)
S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)
Thus Option A is correct.
B) Side Q'S' lies on a line with a slope of -1
Q' (-6, 6)
S' (-2, 2)
coordinate (x, y)
Slope = m = (change in y)/(change in x)
m = (6-2)/[-6-(-2)]
m = 4/(-6+2) = 4/-4
m = -1
Option B is correct
c) QR is longer than Q'R'
Length of QR (-3 to 2) = 5
Length of Q'R' (-6 to 4) = 10
QR is not longer than Q'R'
Option C is false
d) The vertices of the image are closer to the origin than those of the pre-image.
From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.
Option D is False
e) The distance from Q' to the origin is twice the distance from Q to the origin.
The distance from Q' to the origin (6 to 0) = 6
The distance from Q to the origin (3 to 0) = 3
The distance from Q' to the origin = 2(the distance from Q to the origin)
Option E is correct.
Read more about Dilated Objects at; https://brainly.com/question/10253650
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