Question

The rule T 5, -0.5° Ro, 1800(x, ) is applied to FGH to

produce F"G"H". what are the coordinates of vertex F" of F"G"H"?

Answer 1

Based on the sequence of transformation, the coordinates of vertex F" of F"G"H" are F" (4, -1.5).

In Euclidean Geometry, the mapping rule for the rotation of a geometric figure about the origin by 180° in a clockwise or counterclockwise direction can be modeled by the following mathematical expression:

(x, y) → (-x, -y)

Point F (1, 1) → Point F' (-1, -1)

Next, we would apply a translation 5 units to the right and 0.5 unit down to the new figure (△F'G'H'), in order to determine the coordinates of vertex F" of its image as follows;

(x, y) → (x + 5, y - 0.5)

PointF" (-1, -1) → (-1 + 5, -1 - 0.5) = F" (4.5, -1.5).

In conclusion, we can logically deduce that the point (4.5, -1.5) represent the coordinates of vertex F" of triangle F"G"H".

Answer 2

Explanation:

Given rule for the multiple translations is,

`T_(5,-0.5).R_(0.180^(\circ))(x,y)`

Apply the rule
`R_(0,180^(\circ))` first.

(x, y) → (-x, -y)

This rule illustrates a rotation of the triangle FGH by 180° about the origin,

Vertices of ΔFGH are,

F → (1, 1)

G → (4, 5)

H → (5, 1)

After rotation vertices of the image triangle are,

F' → (-1, -1)

G' → (-4, -5)

H' → (-5, -1)

Further apply the rule,

`T_(5,-0.5)`

(x, y) → (x + 5, y - 0.5)

By this rule of translation,

F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}

→ F"(4, -1.5)

G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]

→ G"(1, -5.5)

H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]

→ H"(0, -1.5)