Question

problem 1 here is triangle a. draw a dilation of triangle a where the image has a larger area.

Explanation:

Step1: Recall dilation rule

To increase the area of a triangle by dilation, we use a scale - factor \(k> 1\).

Step2: Choose a scale - factor

Let's choose \(k = 2\) for simplicity.

Step3: Identify triangle vertices

Let the vertices of triangle \(A\) be \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\).

Step4: Apply dilation formula

The new vertices \((x_1',y_1')\), \((x_2',y_2')\), \((x_3',y_3')\) after dilation with scale - factor \(k\) about the origin are given by \((x_i',y_i')=(k x_i,k y_i)\) for \(i = 1,2,3\). Then connect the new vertices to form the dilated triangle.

Answer:

Draw a new triangle with vertices obtained by multiplying the coordinates of the vertices of triangle \(A\) by a scale - factor \(k>1\) (e.g., \(k = 2\)) and connect them.