Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation

Question

Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo’s line?

line on coordinate plane passing through negative 1 comma 0 and 0 comma 2

y − F = −2(x − G)y
y + F = 2(x + G)
y − G = −one half(x − F)
y − G = −one half(x + F)

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Nguyệt Ánh 4 years 2021-08-28T00:54:12+00:00 1 Answers 2 views 0

Answers ( )

  1. thienthi
    0
    2021-08-28T00:55:12+00:00
    Reply

    Answer:

    C

    Step-by-step explanation:

    The line shown on the grid passes through the points (-1, 0) and (0, 2).

    Remember that the slopes of perpendicular lines are negative reciprocals of each other. So, find the slope of the line on the grid first. We can use the slope formula:

    \displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{0-(-1)}=\frac{2}{1}=2

    So, the slope of the line on the grid is two.

    To find the negative reciprocal of two, we flip it and add a negative. We can rewrite 2 as 2/1. Therefore, the slope of the perpendicular line is -1/2.

    We are also given that the line passes through the point (F, G). Since we know the slope and a point, we can use the point-slope form:

    y-y_1=m(x-x_1)

    Where m is the slope and (x₁, y₁) is a point.

    Let (F, G) be (x₁, y₁). Substitute:

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

    Therefore, our answer is C.

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