Triangle QRS is dilated according to the rule DO,2 (x,y). On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R
S has points (negative 3, 3), (2, 4), and (negative 1, 1). What is true about the image ΔQ'R'S'? Select three options. Which statements are true? DO,2 (x,y) = (2x, 2y) Side Q'S' lies on a line with a slope of -1. QR is longer than Q'R'. The vertices of the image are closer to the origin than those of the pre-image. The distance from Q' to the origin is twice the distance from Q to the origin.
2 answers:
Answer:
Options A, B and E are correct
Step-by-step explanation:
From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.
The scale factor is 2
QRS → Q'R'S' = (x,y) → 2(x,y)
The coordinates of ∆QRS
Q (-3, 3)
R (2, 4)
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 order 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,
we would graph the coordinates of the two triangles.
Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.
See attached the diagram for better explanation.
Let's check out each options and compare it with diagram we obtained:
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)
This option 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)]
= 4/(-6+2) = 4/-4
m = -1
This option 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'
This option is false
d) The vertices of the image are closer to the origin than those of the pre-image
The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.
From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.
This option 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)
This option is correct
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