Question

if the triangle is translated so that z becomes z(-2, -3), then x becomes ______.

x(2, -6)
x(2, -2)
x(0, -2)
x(2, 0)
2 multiple choice 4 points
which of the following will map △abc onto △abc?

reflection in the x - axis
reflection in the y - axis
translation 2 units right and 1 unit up
clockwise turn 90° about the origin

Explanation:

First Question

Step1: Identify Z's original coordinates

From the grid, $Z = (-4, 1)$

Step2: Find translation vector

Let translation be $(h,k)$. Use $Z' = Z + (h,k)$:

$$\begin{cases}-4 + h = -2 \\ 1 + k = -3\end{cases}$$

Solve: $h = -2 - (-4) = 2$, $k = -3 - 1 = -4$
Translation vector: $(2, -4)$

Step3: Identify X's original coordinates

From the grid, $X = (0, 2)$

Step4: Calculate X' coordinates

$X' = (0 + 2, 2 + (-4)) = (2, -2)$

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Second Question

1. Pick a reference point, e.g., $A(0,1)$ maps to $A'(2,2)$.
2. Calculate change: $2-0=2$ (right 2 units), $2-1=1$ (up 1 unit).
3. Verify with other points: $B(-2,1)\to B'(0,2)$ (2 right, 1 up), $C(-2,4)\to C'(2,5)$ (2 right,1 up). This matches the translation rule, and no other transformation (reflection, rotation) aligns the triangles.

Answer:

$X'(2,-2)$