Respuesta :
Given:
Consider the vertices of the triangle are (4,4) (6,7) and (8,0).
The triangle is dilated by a scale factor of 3.
To find:
The vertices of the new triangle after dilation.
Solution:
If a figure is dilated by scale factor k with origin as the center of dilation, then the rule of dilation is:
[tex](x,y)\to (kx,ky)[/tex]
The given figure is dilated by scale factor 3 with origin as the center of dilation, then the rule of dilation is:
[tex](x,y)\to (3x,3y)[/tex]
Let the vertices of the triangle are A(4,4), B(6,7) and C(8,0).
Using this rule of dilation, we get
[tex]A(4,4)\to A'(3(4),3(4))[/tex]
[tex]A(4,4)\to A'(12,12)[/tex]
Similarly,
[tex]B(6,7)\to B'(3(6),3(7))[/tex]
[tex]B(6,7)\to B'(18,21)[/tex]
And,
[tex]C(8,0)\to C'(3(8),3(0))[/tex]
[tex]C(8,0)\to C'(24,0)[/tex]
The vertices of the new triangle are (12,12), (18,21), (24,0).
Therefore, the correct option is 4.
