Question

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△klm is dilated by a scale factor of 2 with the center of dilation at the origin. what are the coordinates of point k?

Explanation:

Step1: Find the coordinates of point \( K \)

From the graph, the coordinates of point \( K \) are \( (1,5) \).

Step2: Apply the dilation formula

When a point \( (x,y) \) is dilated by a scale factor \( k \) with the center of dilation at the origin, the formula for the new coordinates \( (x',y') \) is \( x'=k\times x \) and \( y' = k\times y \). Here \( k = 2 \), \( x = 1 \), \( y=5 \).
So \( x'=2\times1=2 \) and \( y'=2\times5 = 10 \).

Answer:

\((2,10)\)