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A triangle has vertices on a coordinate grid at F(3,-2),G(3,9), and H(-6,-2). What is the length, in units, of bar(FG) ? Answer: units

A triangle has vertices on a coordinate grid at F(3,−2),G(3,9) F(3,-2), G(3,9) , and H(−6,−2) H(-6,-2) . 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(3,−2),G(3,9) F(3,-2), G(3,9) , and H(−6,−2) H(-6,-2) . What is the length, in units, of FG‾ \overline{F G} ?\newlineAnswer: □\square units
  1. Identify Points F and G: Identify the coordinates of points F and G. F(3,−2)F(3,-2) and G(3,9)G(3,9) are the points we are interested in.
  2. Calculate Length of FG: 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.\newlineThe distance formula is 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 the two points.
  4. Substitute Coordinates: Substitute the coordinates of F and G into the distance formula.\newlineFor F(33,−2-2) and G(33,99), we have d=(3−3)2+(9−(−2))2d = \sqrt{(3 - 3)^2 + (9 - (-2))^2}.
  5. Simplify Expression: Simplify the expression. d=(0)2+(11)2=0+121=121d = \sqrt{(0)^2 + (11)^2} = \sqrt{0 + 121} = \sqrt{121}.
  6. Calculate Square Root: Calculate the square root of 121121.d=121=11d = \sqrt{121} = 11.
  7. State Length of FGFG: State the length of bar(FGFG).\newlineThe length of bar(FGFG) is 1111 units.

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