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Point D

and Point F
have the same second coordinate, and ECFD
is a quadrilateral. What coordinates would Point F
be plotted at to make line segment FD
have a length of 2 cm?

(1 point)
Responses

(1, −1)
left parenthesis 1 comma negative 1 right parenthesis

(−1, 0)
left parenthesis negative 1 comma 0 right parenthesis

(−1, 1)
left parenthesis negative 1 comma 1 right parenthesis

(−2, 2)

Given:
E (-2,3)
C-1,2)
D (-3,1)

1 answer

To determine the coordinates of Point F such that the line segment FD has a length of 2 cm, we first need to find the coordinates of Point D, which is given as D(-3, 1).

Since point F has the same second coordinate as point D, this means the y-coordinate of F will also be 1. Therefore, the coordinates of point F will be in the form F(x, 1).

Now, we need to find the x-coordinate of F such that the distance FD is 2 cm. The distance formula between points D(-3, 1) and F(x, 1) is given by:

\[ \text{Distance} = \sqrt{(x - (-3))^2 + (1 - 1)^2} \]

This simplifies to:

\[ \text{Distance} = \sqrt{(x + 3)^2} \]

Since we want this distance to be equal to 2:

\[ \sqrt{(x + 3)^2} = 2 \]

Squaring both sides results in:

\[ (x + 3)^2 = 4 \]

Taking the square root of both sides gives us two possible equations:

  1. \(x + 3 = 2\)
  2. \(x + 3 = -2\)

Solving these equations:

  1. \(x + 3 = 2\) leads to \(x = -1\)
  2. \(x + 3 = -2\) leads to \(x = -5\)

Thus, the coordinates of Point F can be either (-1, 1) or (-5, 1).

Now, looking at the response choices you provided:

  • (1, -1)
  • (-1, 0)
  • (-1, 1) <-- This is one of our solutions.
  • (-2, 2)

The coordinate that satisfies the required condition is (-1, 1).