Question

directions: answer the following questions to the best of your ability. for the y-axis, use the same scaling as the x-axis

1. in math, the word dilate means to ____ or ____ a figure.
2. if a scale factor is less than 1, then your figure gets ____________
3. if a scale factor is greater than 1, then your figure gets ____________
4. graph the dilated image of triangle jkl using a scale factor of 2 and (0,0) as the center of dilation.

j: __________ j: __________
k: __________ k: __________
l: __________ l: __________

1. graph the dilated image of quadrilateral mnop using a scale factor of 3 and the origin as the center of dilation.

m: __________ m: __________
n: __________ n: __________
o: __________ o: __________
p: __________ p: __________

Explanation:

Step1: Define dilation

Dilation is a transformation that resizes a figure, making it larger or smaller while keeping its shape.

Step2: Analyze scale factor <1

When the scale factor $0

Step3: Analyze scale factor >1

When the scale factor $k>1$, the figure enlarges.

Step4: Identify triangle JKL coordinates

From the graph:
$J=(2, 4)$, $K=(1, 1)$, $L=(4, 1)$

Step5: Dilate triangle JKL

Multiply each coordinate by scale factor 2, center $(0,0)$:
$J'=(2\times2, 4\times2)=(4, 8)$
$K'=(1\times2, 1\times2)=(2, 2)$
$L'=(4\times2, 1\times2)=(8, 2)$

Step6: Identify quadrilateral MNOP coordinates

From the graph:
$M=(1, 3)$, $N=(3, 2)$, $O=(2, -2)$, $P=(-1, 0)$

Step7: Dilate quadrilateral MNOP

Multiply each coordinate by scale factor 3, center $(0,0)$:
$M'=(1\times3, 3\times3)=(3, 9)$
$N'=(3\times3, 2\times3)=(9, 6)$
$O'=(2\times3, -2\times3)=(6, -6)$
$P'=(-1\times3, 0\times3)=(-3, 0)$

Answer:

1. enlarge; shrink
2. smaller
3. larger

4.
$J$: $(2, 4)$; $J'$: $(4, 8)$
$K$: $(1, 1)$; $K'$: $(2, 2)$
$L$: $(4, 1)$; $L'$: $(8, 2)$
(Graph: Plot points $(4,8)$, $(2,2)$, $(8,2)$ and connect them to form the dilated triangle)
5.
$M$: $(1, 3)$; $M'$: $(3, 9)$
$N$: $(3, 2)$; $N'$: $(9, 6)$
$O$: $(2, -2)$; $O'$: $(6, -6)$
$P$: $(-1, 0)$; $P'$: $(-3, 0)$
(Graph: Plot points $(3,9)$, $(9,6)$, $(6,-6)$, $(-3,0)$ and connect them to form the dilated quadrilateral)