Question

refer to the figure below. if the triangle is reflected across the y - axis, the coordinates of the new vertices will be (5,0), (2,3), and ______.
(0,5)
(2,3)
(4,3)
(3,5)
4 multiple choice 4 points
△abc is the image of △abc after translation of 3 units left and 4 units down. what are the coordinates of each vertex of △abc?
a(1, - 2), b(0,2), c(-2,0)
a(1,1), b(0,5), c(-2,3)
a(2, - 3), b(1,1), c(-1, - 1)
a(5, - 2), b(4,2), c(2,0)

Explanation:

First Question

Step1: Identify original vertices

First, find the original vertices of the triangle from the grid: (-5, 0), (-2, 3), (-4, 3)

Step2: Apply y-axis reflection rule

The rule for reflecting across the y-axis is $(x,y)\to(-x,y)$.
For $(-5,0)$: $-(-5)=5$, so $(5,0)$
For $(-2,3)$: $-(-2)=2$, so $(2,3)$
For $(-4,3)$: $-(-4)=4$, so $(4,3)$

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Second Question

Step1: Identify original vertices

From the grid, original vertices are: $A(4,2)$, $B(3,6)$, $C(1,4)$

Step2: Apply translation rule

Translation rule: $(x,y)\to(x-3,y-4)$ (3 left, 4 down)
For $A(4,2)$: $4-3=1$, $2-4=-2$ → $A'(1,-2)$
For $B(3,6)$: $3-3=0$, $6-4=2$ → $B'(0,2)$
For $C(1,4)$: $1-3=-2$, $4-4=0$ → $C'(-2,0)$

Answer:

(4, 3)