The small triangle's coordinates are (2,2), (6,4), and (4,6). The large triangle's coordinates are (5,5), (15,10), and (10,15).
Using the formula (x2, y2) = (kx1, ky1), we can pick one coordinate from each triangle to solve for k. Let's pick the points (2,2) and (5,5) to find k:
(5,5) = k(2,2)
(5,5) = (2k,2k)
Now we can see that k = 5/2 = 2.5.
Therefore, the value of k is 2.5.
Use the image to answer the question.
An illustration shows two coordinate grids side by side, both showing the first quadrant. The x-axis and y-axis range from 0 to 16 in increments of 1, but are labeled in increments of 2. The first grid shows a solid line triangle connecting the coordinates left parenthesis 2 comma 2 right parenthesis, left parenthesis 6 comma 4 right parenthesis, and left parenthesis 4 comma 6 right parenthesis. The second grid shows a solid line triangle connecting the coordinates left parenthesis 5 comma 5 right parenthesis, left parenthesis 15 comma 10 right parenthesis, and left parenthesis 10 comma 15 right parenthesis. The coordinates are not labeled.
The small triangle has been dilated to produce the larger triangle using the algebraic formula (x2,y2)=(kx1,ky1) . What is the value of k ?
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