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A triangle has vertices on a coordinate grid at F(1,-1),G(1,3), and H(-8,-1). What is the length, in units, of bar(FG) ? Answer: units

A triangle has vertices on a coordinate grid at F(1,−1),G(1,3) F(1,-1), G(1,3) , and H(−8,−1) H(-8,-1) . What is the length, in units, of FG‾ \overline{F G} ?\newlineAnswer: □\square units

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Q. A triangle has vertices on a coordinate grid at F(1,−1),G(1,3) F(1,-1), G(1,3) , and H(−8,−1) H(-8,-1) . What is the length, in units, of FG‾ \overline{F G} ?\newlineAnswer: □\square units
  1. Identify Coordinates: Identify the coordinates of points FF and GG. F(1,−1)F(1,-1) and G(1,3)G(1,3).
  2. Calculate Length: Recognize that the length of bar(FGFG) is the distance between points FF and GG. We will use the distance formula to calculate this length.
  3. Apply Distance Formula: Apply the distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of points F and G, respectively.
  4. Substitute Coordinates: Substitute the coordinates of F and G into the distance formula.\newlined=(1−1)2+(3−(−1))2d = \sqrt{(1 - 1)^2 + (3 - (-1))^2}
  5. Simplify Expression: Simplify the expression inside the square root. d=(0)2+(4)2d = \sqrt{(0)^2 + (4)^2}
  6. Calculate Distance: Calculate the distance.\newlined=0+16d = \sqrt{0 + 16}\newlined=16d = \sqrt{16}\newlined=4d = 4

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