Question

draw the image of \\( \triangle abc \\) for the dilation with center \\( o \\) and scale factor 2.
choose the correct graph below.
o a.
o b.
o c.
o d.

Explanation:

Step1: Understand dilation

Dilation is a transformation that changes the size of a figure. The formula for dilation with center \((x_0,y_0)\) and scale factor \(k\) is \((x,y)\to(x_0 + k(x - x_0),y_0 + k(y - y_0))\).

Step2: Analyze each vertex

Let's assume the vertices of \(\triangle ABC\) are \(A(x_1,y_1)\), \(B(x_2,y_2)\), \(C(x_3,y_3)\). After dilation with scale factor \(2\) and center \(O\), the new vertices \(A'(x_0+2(x_1 - x_0),y_0 + 2(y_1 - y_0))\), \(B'(x_0+2(x_2 - x_0),y_0 + 2(y_2 - y_0))\), \(C'(x_0+2(x_3 - x_0),y_0 + 2(y_3 - y_0))\). This means the distance from each vertex to the center \(O\) is doubled.

Step3: Check the options

Option C has the triangle \(\triangle ABC\) dilated such that the distance from each vertex to the center \(O\) is twice the original distance.

Answer:

C.