Mathematics, 18.11.2020 14:00, nick974

The vertices of a rectiſngle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5,1). A translation maps R to the point (-4, 2). Find the translation rule and the image of U.

Answers: 3

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answered: punkinrichard1oxon2i

The translation rule is T (x, y) → (x + 1, y + 7)

The image of point U is (-4, 8)

Step-by-step explanation:

Let us revise the rule of translation

If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)If the point (x, y) translated vertically up by k units then its image is (x, y + k)→ (x + h, y) ⇒ T (x, y) → (x, y + k)If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)

∵ Point R = (-5, -5)

∵ Point R' = (-4, 2)

∵ -4 > -5 and 2 > -5

→ That means point R translated to the right and up T (x, y) → (x + h, y + k)

∴ h = -4 - (-5) = -4 + 5 = 1 unit

∴ k = 2 - (-5) = 2 + 5 = 7 units

→ By using the 1st and 3rd rules above

∴ The translation rule is T (x, y) → (x + 1, y + 7)

∵ Point U = (-5, 1)

→ By using the rule of translation above

∴ U' = (-5 + 1, 1 + 7)

∴ U' = (-4, 8)

∴ The image of point U is (-4, 8)

answered: Guest

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step-by-step explanation:

answered: Guest

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2 = -20

divide by -2 on each side

-2x^2 /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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The vertices of a rectiſngle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5,1). A translation maps R t...