Question

triangle A”B”C” is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship between BC and B”C”

Answers

  1. Answer:
    the equation that explains the relationship between BC and B”C” is:
    BC = 2 * B”C”
    This equation states that the length of BC is equal to twice the length of B”C”.
    Step-by-step explanation:
    If triangle A”B”C” is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin, then the coordinates of the vertices of triangle A”B”C” can be expressed as follows:
    A” (x+1, y+1)
    B” (3x+3, 3y+3)
    C” (3x+6, 3y+6)
    To find the equation that explains the relationship between BC and B”C”, we can use the distance formula to find the length of both segments. The distance formula is:
    distance = √((x2 – x1)^2 + (y2 – y1)^2)
    Where (x1, y1) and (x2, y2) are the coordinates of the two points.
    Using the distance formula, we can find the length of BC as follows:
    BC = √((3x – x)^2 + (3y – y)^2)
    = √((2x)^2 + (2y)^2)
    = √(4x^2 + 4y^2)
    = 2√(x^2 + y^2)
    We can also find the length of B”C” as follows:
    B”C” = √((3x+6 – 3x-3)^2 + (3y+6 – 3y-3)^2)
    = √((3)^2 + (3)^2)
    = √(9 + 9)
    = √(18)
    = 3√(2)

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