Answer:
The two figures below are not similar
Step-by-step explanation:
we know that
If the two figures are similar
then
the ratio of their corresponding sides are equal
[tex]\frac{CD}{IJ}=\frac{DE}{JK}[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance CD
[tex]C(-4,2)\\D(-1,2)[/tex]
substitute the values
[tex]d=\sqrt{(2-2)^{2}+(-1+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(3)^{2}}[/tex]
[tex]dCD=3\ units[/tex]
Step 2
Find the distance IJ
[tex]I(2,1)\\J(4,1)[/tex]
substitute the values
[tex]d=\sqrt{(1-1)^{2}+(4-2)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(2)^{2}}[/tex]
[tex]dIJ=2\ units[/tex]
Step 3
Find the distance DE
[tex]D(-1,2)\\E(0,0)[/tex]
substitute the values
[tex]d=\sqrt{(0-2)^{2}+(0+1)^{2}}[/tex]
[tex]d=\sqrt{(-2)^{2}+(1)^{2}}[/tex]
[tex]dED=\sqrt{5}\ units[/tex]
Step 4
Find the distance JK
[tex]J(4,1)\\K(5,0)[/tex]
substitute the values
[tex]d=\sqrt{(0-1)^{2}+(5-4)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(1)^{2}}[/tex]
[tex]dJK=\sqrt{2}\ units[/tex]
Step 5
Find the ratios of the corresponding sides
Remember that
If the figures are similar
then
the ratio of their corresponding sides are equal
[tex]\frac{CD}{IJ}=\frac{DE}{JK}[/tex]
we have
[tex]dCD=3\ units[/tex]
[tex]dIJ=2\ units[/tex]
[tex]dED=\sqrt{5}\ units[/tex]
[tex]dJK=\sqrt{2}\ units[/tex]
Substitute
[tex]\frac{3}{2}\neq \frac{\sqrt{5}}{\sqrt{2}}[/tex]
therefore
the figures are not similar
