Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y – 3.5) to create the image ΔA'B'C' shown on the coordinate plane. Which graph shows the pre-image, ΔABC?coordinates are C (-5,-10), B(-1,-1),A(-1,2)

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23-04-2017
Mathematics

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Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y – 3.5) to create the image ΔA'B'C' shown on the coordinate plane. Which graph shows the pre-image, ΔABC?coordinates are C (-5,-10), B(-1,-1),A(-1,2)

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taskmasters taskmasters · Answer 1 · 2017-05-06T16:58:47+02:00

Given:
ΔA'B'C' image.
A (-1,2)
B (-1,-1)
C (-5,-10)

rule of translation(x,y) → (x + 1.5,y - 3.5)

This means that the given coordinates are the the sum of x and the difference of y.

A:
-1 = x + 1.5 → -x = 1.5 + 1 → -x = 2.5 → -x/-1 = 2.5/-1 → x = -2.5
2 = y - 3.5 → -y = -3.5 - 2 → -y = -5.5 → -y/-1 = -5.5/-1 → y = 5.5
A (-2.5 , 5.5)

B:
-1 = x + 1.5 → -x = 1.5 + 1 → -x = 2.5 → -x/-1 = 2.5/-1 → x = -2.5
-1 = y - 3.5 → -y = -3.5 + 1 → -y = -2.5 → -y/-1 = -2.5/-1 → y = 2.5
B (-2.5,2.5)

C:
-5 = x + 1.5 → -x = 1.5 + 5 → -x = 6.5 → -x/-1 = 6.5/-1 → x = -6.5
-10 = y - 3.5 → -y = -3.5 + 10 → -y = 6.5 → -y/-1 = 6.5/-1 → y = -6.5
C (-6.5, -6.5)

The pre image will have the following coordinates:
A (-2.5 , 5.5) ; B (-2.5,2.5) ; C (-6.5, -6.5)

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-22T07:18:42+01:00

Triangle ABC was translated to create the image ΔA'B'C'. The pre-image coordinates of the ΔABC is A(-2.5, 5.5), B(-2.5, 2.5) and C(-6.5, -6.5) and graph attached below.

What is the transformation of figure?

Transformation of a figure is to change the size, shape or the position of a figure to create a new figure for required use.

Triangle ABC was translated according to the rule

[tex](x, y) --> (x + 1.5, y - 3.5)[/tex]

The translated triangle is ΔA'B'C' and the coordinates of ΔABC is A(-1,2), B(-1,-1), and C (-5,-10).

The rule of the translation of triangle ABC is,

[tex](x, y) --> (x + 1.5, y - 3.5)[/tex]

The above rule suggest that, the transformation of the triangle is done by adding 1.5 in its x coordinates and subtracting 3.5 from its y coordinates.

Thus to find the pre-image, we need to subtract the 1.5 and add 3.5 from x and y coordinates receptively.

Applying this transformation on coordinates A(-1,2), B(-1,-1), and C (-5,-10), we get,

[tex]A=A'(-1-1.5,2+3.5)=(-2.5, 5.5)\\B=B'(-1-1.5,-1+3.5)=(-2.5, 2.5)\\C=C'(-5-1.5,-10+3.5)=(-6.5, -6.5)[/tex]

Thus, coordinates of the ΔABC is A(-2.5, 5.5), B(-2.5, 2.5) and C(-6.5, -6.5)

Learn more about the transformation of figure here;

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