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:
![(x,y)\to (kx,ky)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28kx%2Cky%29)
The given figure is dilated by scale factor 3 with origin as the center of dilation, then the rule of dilation is:
![(x,y)\to (3x,3y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%283x%2C3y%29)
Let the vertices of the triangle are A(4,4), B(6,7) and C(8,0).
Using this rule of dilation, we get
![A(4,4)\to A'(3(4),3(4))](https://tex.z-dn.net/?f=A%284%2C4%29%5Cto%20A%27%283%284%29%2C3%284%29%29)
![A(4,4)\to A'(12,12)](https://tex.z-dn.net/?f=A%284%2C4%29%5Cto%20A%27%2812%2C12%29)
Similarly,
![B(6,7)\to B'(3(6),3(7))](https://tex.z-dn.net/?f=B%286%2C7%29%5Cto%20B%27%283%286%29%2C3%287%29%29)
![B(6,7)\to B'(18,21)](https://tex.z-dn.net/?f=B%286%2C7%29%5Cto%20B%27%2818%2C21%29)
And,
![C(8,0)\to C'(3(8),3(0))](https://tex.z-dn.net/?f=C%288%2C0%29%5Cto%20C%27%283%288%29%2C3%280%29%29)
![C(8,0)\to C'(24,0)](https://tex.z-dn.net/?f=C%288%2C0%29%5Cto%20C%27%2824%2C0%29)
The vertices of the new triangle are (12,12), (18,21), (24,0).
Therefore, the correct option is 4.