Question

i can use algebraic representations to explain the effect of transformations.
for 23-24, use the coordinates to describe the transformation and write a rule.
23.

pre-image	image
b(-3, -6)	b(-3, 6)
c(-2, -2)	c(-2, 2)

description:
rule:

24.

pre-image	image
h(-4, 8)	h(-8, -4)
i(-3, 5)	i(-5, -3)

description:
rule:

i can describe the effect of dilations on linear and area measurements.

1. a figure will be dilated by a scale factor of 1.4. how will this affect the following:

a. the perimeter of the figure?
b. the area of the figure?

1. a figure will be dilated by a scale factor of $\frac{8}{7}$. how will this affect the following:

a. the perimeter of the figure?
b. the area of the figure?

1. a figure has a perimeter of 26 units. what will the new perimeter be after a dilation with a scale factor of 2.5?

1. a figure has a perimeter of 112 units. what will the new perimeter be after a dilation with a scale factor of $\frac{1}{4}$?

1. a figure has an area of 50 units$^2$. what will the new area be after a dilation with a scale factor of 3?

1. a figure has an area of 125 units$^2$. what will the new area be after a dilation with a scale factor of $\frac{1}{5}$?

Explanation:

Step1: Analyze Q23 coordinate changes

Compare pre-image/image coordinates:
$A(-6,-2)\to A'(-6,2)$, $B(-3,-6)\to B'(-3,6)$, $C(-2,-2)\to C'(-2,2)$

Step2: Describe Q23 transformation

x-values stay, y-values flip sign.

Step3: Write Q23 rule

$(x,y)\to(x,-y)$

Step4: Analyze Q24 coordinate changes

Compute differences:
$G(-2,7)\to G'(-7,-2)$: $-2-5=-7$, $7-9=-2$
$H(-4,8)\to H'(-8,-4)$: $-4-4=-8$, $8-12=-4$
$I(-3,5)\to I'(-5,-3)$: $-3-2=-5$, $5-8=-3$
Wait, correct pattern: $x\to x-5$, $y\to y-9$ (consistent shift)

Step5: Describe Q24 transformation

Shift left 5, down 9 units.

Step6: Write Q24 rule

$(x,y)\to(x-5,y-9)$

Step7: Q25a: Perimeter dilation effect

Perimeter scales with scale factor.
New perimeter = $1.4\times$ original

Step8: Q25b: Area dilation effect

Area scales with square of scale factor.
New area = $(1.4)^2\times$ original = $1.96\times$ original

Step9: Q26a: Perimeter dilation effect

Perimeter scales with $\frac{8}{7}$.
New perimeter = $\frac{8}{7}\times$ original

Step10: Q26b: Area dilation effect

Area scales with $(\frac{8}{7})^2$.
New area = $\frac{64}{49}\times$ original

Step11: Q27: Calculate new perimeter

New perimeter = $26\times2.5$
$=65$

Step12: Q28: Calculate new perimeter

New perimeter = $112\times\frac{1}{4}$
$=28$

Step13: Q29: Calculate new area

New area = $50\times3^2$
$=50\times9=450$

Step14: Q30: Calculate new area

New area = $125\times(\frac{1}{5})^2$
$=125\times\frac{1}{25}=5$

Answer:

23.
Description: Reflection over the x-axis
Rule: $(x,y)\to(x,-y)$

24.
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