Question

in the diagram, m and m are congruent.
which of the following is not a way of transforming m into m ?
a reflection across the x-axis, then a reflection across the y-axis
a reflection across the y-axis, then a translation down 2 units
a rotation of 180° about the origin
a translation down 8 units, then a translation right 10 units
question 2
1 pts
△stv has vertices s(-3, -2), t(-4, 3) and v(-2, 3). if (x, y) → (x + 2, y - 3), what are the vertices of its image?
s(0, 1), t(-1, 6), v(0, 5)
s(3, 2), t(4, -3), v(2, -3)
s(-1, -5), t(-2, 0), v(0, 0)
s(-5, 1), t(-6, 6), v(-4, 6)

Explanation:

Question 1 (Transforming M into M')

Step1: Analyze each option

• Option 1: Reflect across x - axis then y - axis

Reflecting a point \((x,y)\) across x - axis gives \((x, -y)\), then across y - axis gives \((-x, -y)\), which is equivalent to a \(180^\circ\) rotation about the origin. This can transform M to M'.

• Option 2: Reflect across y - axis then translate down 2 units

Reflecting M across y - axis would place it on the right side but at the same vertical level. Translating down 2 units does not match the vertical shift of M' (M' is much lower). So this is not a valid transformation.

• Option 3: Rotation of \(180^\circ\) about origin

A \(180^\circ\) rotation \((x,y)\to(-x, -y)\) can map M to M' as seen from the diagram.

• Option 4: Translate down 8 units then right 10 units

By visually checking the grid, moving M down 8 units and right 10 units aligns with M'.

Step1: Apply the transformation \((x,y)\to(x + 2,y - 3)\) to each vertex

• For \(S(-3,-2)\):

\(x'=-3 + 2=-1\), \(y'=-2-3=-5\), so \(S'(-1,-5)\).

• For \(T(-4,3)\):

\(x'=-4 + 2=-2\), \(y'=3-3 = 0\), so \(T'(-2,0)\).

• For \(V(-2,3)\):

\(x'=-2 + 2=0\), \(y'=3-3 = 0\), so \(V'(0,0)\).

Answer:

a reflection across the y - axis, then a translation down 2 units

Question 2 (Transforming \(\triangle STV\))