Write the equation of a line over which A(-3,5) reflects to A’(2,-5). BRAINLIEST TO THE 1ST PERSON!!

Question

Write the equation of a line over which A(-3,5) reflects to A’(2,-5). BRAINLIEST TO THE 1ST PERSON!!

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Answers ( No )

    0
    2021-09-14T17:32:13+00:00

    Given two points:
    A = (x₁,y₁) = (-3,5)
    A’ = (x₂,y₂) = (2,-5)

    Find the midpoint of point A and point A’
    The midpoint of the two points lies on the reflection line. You can find the midpoint by this following formula
    x midpoint = \dfrac{x_{1}+x_{2}}{2}
    y midpoint = \dfrac{y_{1}+y_{2}}{2}

    Plug in the numbers
    x midpoint = \dfrac{-3+2}{2}
    x midpoint = \dfrac{-1}{2}
    x midpoint = -0.5

    y midpoint = \dfrac{5+(-5)}{2}
    y midpoint = \dfrac{0}{2}
    y midpoint = 0

    The midpoint is
    (x,y) = (-0.5, 0)

    Find the slope of the line passes through (-3,5) and (2,-5)
    Use this following formula to find the slope
    m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

    Plug in the numbers
    m = \dfrac{-5-5}{2-(-3)}
    m = \dfrac{-10}{2+3}
    m = -10/5
    m = -2

    Find the slope of the line which is perpendicular to the line that passes through (-3,5) and (2,-5)
    The line whose slope we want to find is the reflection line we are looking for. Two perpendicular lines have the rule of slope as follows.
    m₁ × m₂ = -1

    Input the numbers
    -2 × m₂ = -1
    m₂ =  \dfrac{-1}{-2}
    m₂ =  \dfrac{1}{2}

    Find the line equation
    The reflection line has the slope of 1/2 and passes through the midpoint (-0.5, 0)
    The formula to find a line equation:
    y – y₁ = m(x – x₁)

    Input the numbers (m = 1/2, x₁ = -0.5, y = 0)
    y – y₁ = m(x – x₁)
    y – 0 = 1/2 (x – (-0.5))
    y = 1/2 (x + 0.5)
    y = \frac{1}{2}x+0.25
    This is the line equation

    0
    2021-09-14T17:32:19+00:00

    Not sure but (-2,5) and (1,3)

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