17. Graph the image of the quadrilateral below using a scale factor of k = 2/3, using the origin as the center of dilation. 19. P'(-2, -5) is the image of P after a translation along the rule (x, y) ? (x + 1, y + 2). What are the coordinates of P?
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Let's assume the vertices are \( C(x_1, y_1) \), \( D(x_2, y_2) \), \( E(x_3, y_3) \), and \( F(x_4, y_4) \). Show more…
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Select the correct answers from each drop-down menu to complete the steps in the proof that show quadrilateral KITE with vertices K(0, -2), I(2, 7), and E(4, -1) is a kite. Using the distance formula, KI = ∑((2-0)^2 + (7-(-2))^2) = ∑(4 + 81) = ∑85. KE = ∑((4-0)^2 + (-1-(-2))^2) = ∑(16 + 1) = ∑17. IT = ∑((2-4)^2 + (7-(-1))^2) = ∑((-2)^2 + 8^2) = ∑68. TE = ∑((4-2)^2 + (-1-7)^2) = ∑(2^2 + (-8)^2) = ∑68. Therefore, KITE is a kite because KI = KE and IT = TE.
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A quadrilateral is reflected across the $y$ -axis. The coordinates of the vertices are $P^{\prime}(-2,2), Q^{\prime}(4,1), R^{\prime}(-1,-5),$ and $S^{\prime}(-3,-4) .$ What were the coordinates of the quadrilateral in its original position?
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In Exercises $17-20,$ graph the quadrilateral with the given vertices in a coordinate plane. Then show that the quadrilateral is a parallelogram. (See Example $5 .$ ) $$\mathrm{N}(-5,0), \mathrm{P}(0,4), \mathrm{Q}(3,0), \mathrm{R}(-2,-4)$$
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