Question

rectangle quad has coordinates q(4,5), u(4,10), a(11,10), and d(11,5). quad is the image of quad after a dilation with center (0,0) and scale factor 5. what is the length of segment qu?
the length of segment qu is □ unit(s).
(type a whole number.)

Explanation:

Step1: Find the length of segment QU

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(Q(4,5)\) and \(U(4,10)\), \(x_1 = 4,y_1 = 5,x_2 = 4,y_2 = 10\).

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Step2: Use the dilation formula

If a segment of length \(L\) is dilated with a scale factor \(k\), the length of the dilated segment \(L'\) is given by \(L'=k\times L\). Here, \(k = 5\) and \(L=QU = 5\).

$$ Q'U'=5\times5 $$

Answer:

\(25\)