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creativ13 [48]
3 years ago
11

Connor is constructing rectangle ABCD. He has plotted A at (−2, 4), B at (0, 3), and C at (−2, −1). Which coordinate could be th

e location of point D?
D (−5, 1)
D (−4, 0)
D (−3, 11)
D (−2, 2)

Mathematics
1 answer:
ella [17]3 years ago
7 0

Answer:

<h2>D (−4, 0)</h2>

Step-by-step explanation:

The image attached shows all given coordinates. There you can observe that point D must be placed at (-4, 0) to enclose a rectangle.

We can also demonstrate this by finding that sides AD and BC are congruent.

<h3>Side AD.</h3>

d_{AD} =\sqrt{(0-4)^{2}+(-4-(-2))^{2} } =\sqrt{16+4}=\sqrt{20}

<h3>Side BC.</h3>

d_{BC}=\sqrt{(-1-3)^{2} +(-2-0)^{2} }  =\sqrt{16+4}=\sqrt{20}

As you can observe, sides AD and BC are congruent. Therefore, point D must be at (-4,0), to enclose a rectangle.

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Step-by-step explanation:

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Area of the triangle = \sqrt{s (s-a)(s-b)(s-c)} where s = \frac{a + b + c}{2}

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