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patriot [66]
2 years ago
9

Polygon ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to create polygon A′B′C′D′. If the endp

oints of line AB are located at (0, -7) and (8, 8), what is the length of line A'B'?
Use the distance formula to help you decide (picture added)

Mathematics
1 answer:
liq [111]2 years ago
3 0

Answer:

A'B' = 34 units

Step-by-step explanation:

Since the dilatation is centred at the origin , then multiply the coordinates by 2

A' = (2(0), 2(- 7) = (0, - 14 )

B' = (2(8), 2(8) = (16, 16)

Calculate the length using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = A'(0, - 14) and (x₂, y₂ ) = B'(16, 16)

d = \sqrt{(16-0)^2+(16+14)^2}

   = \sqrt{16^2+30^2}

   = \sqrt{256+900}

   = \sqrt{1156}

   = 34

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