Line FG goes through the points (4,9) and (1,3). Which equation represents a line that is perpendicular to FG and passes through the point (

Question

Line FG goes through the points (4,9) and (1,3). Which equation represents a line that is perpendicular to FG and passes through the point (2,0)?
-2x+ y=-4
-2x+y=2
X+2y=2
X+2y=4

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Thu Thảo 4 years 2021-09-03T08:39:18+00:00 2 Answers 87 views 0

Answers ( )

  1. thnahdat
    0
    2021-09-03T08:40:55+00:00
    Reply

    Answer:

    x + 2y= 2

    Step-by-step explanation:

    Given

    Points:

    F = (4,9)

    G = (1,3)

    Required

    Determine the equation of line that is perpendicular to the given points and that pass through (2,0)

    First, we need to determine the slope, m of FG

    m = \frac{y_2 - y_1}{x_2 - x_1}

    Where

    F = (4,9) — (x_1,y_1)

    G = (1,3) — (x_2,y_2)

    m = \frac{3 - 9}{1 - 4}

    m = \frac{- 6}{- 3}

    m =2

    The question says the line is perpendicular to FG.

    Next, we determine the slope (m2) of the perpendicular line using:

    m_2 = -\frac{1}{m}

    m_2 = -\frac{1}{2}

    The equation of the line is then calculated as:

    y - y_1 = m_2(x - x_1)

    Where

    m_2 = -\frac{1}{2}

    (x_1,y_1) = (2,0)

    y - 0 = -\frac{1}{2}(x - 2)

    y = -\frac{1}{2}(x - 2)

    y = -\frac{1}{2}x + 1

    Multiply through by 2

    2y = -x + 2

    Add x to both sides

    x + 2y= -x +x+ 2

    x + 2y= 2

    Hence, the line of the equation is x + 2y= 2

  2. Tryphena
    0
    2021-09-03T08:41:12+00:00
    Reply

    Answer:

    X+2y=2

    Step-by-step explanation:

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )