Answer:
The correct option is 4.
Step-by-step explanation:
It is given vertices are A(−8, 5), B(−5, 5), C(−6, 7) and D(−7, 7). The figure ABCD enlarged and plotted on the coordinate grid as figure JKLM. The vertices of image are J(-6,-8) and M(-3,-2).
The y-coordinate of C and D are same, therefore the y-coordinate of L and M must be same.
Let the coordinate of L be (x,-2).
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AD=\sqrt{(-7-(-8))^2+(7-5)^2}=\srqt{5}[/tex]
[tex]JM=\sqrt{(-3-(-6))^2+(-2-(-8))^2}=\srqt{45}=3\srqt{5}[/tex]
Scale factor is
[tex]\frac{JM}{AD}=\frac{3\sqrt{5}}{\sqrt{5}}=3[/tex]
Therefore the scale factor is 3.
The distance between CD is
[tex]CD=\sqrt{(-7-(-6))^2+(7-7)^2}=1[/tex]
Since the scale factor is 3, therefore the LM is 3 units.
[tex]LM=\sqrt{(x-(-3))^2+(-2-(-2))^2}[/tex]
[tex]3=x+3[/tex]
[tex]x=0[/tex]
The coordinates of LM are (0,-2).
Therefore option 4 is correct.
