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A triangle has vertices on a coordinate grid at A(3,-6),B(-6,-6), and C(-6,-1). What is the length, in units, of bar(AB) ? Answer: units

A triangle has vertices on a coordinate grid at A(3,−6),B(−6,−6) A(3,-6), B(-6,-6) , and C(−6,−1) C(-6,-1) . What is the length, in units, of AB‾ \overline{A B} ?\newlineAnswer: □\square units

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Q. A triangle has vertices on a coordinate grid at A(3,−6),B(−6,−6) A(3,-6), B(-6,-6) , and C(−6,−1) C(-6,-1) . What is the length, in units, of AB‾ \overline{A B} ?\newlineAnswer: □\square units
  1. Identify Points A and B: Identify the coordinates of points A and B. Point A is at (3,−6)(3, -6) and point B is at (−6,−6)(-6, -6).
  2. Use Distance Formula: Recognize that the length of segment AB can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula for two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:\newline(x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  3. Substitute Coordinates: Substitute the coordinates of points AA and BB into the distance formula.\newline(−6−3)2+(−6−(−6))2\sqrt{(-6 - 3)^2 + (-6 - (-6))^2}
  4. Calculate Differences: Calculate the differences for each coordinate. (−9)2+(0)2\sqrt{(-9)^2 + (0)^2}
  5. Square and Add: Square the differences and add them together. 81+0\sqrt{81 + 0}
  6. Simplify Square Root: Simplify the square root to find the distance. 81\sqrt{81}
  7. Calculate Final Value: Calculate the final value of the square root. The square root of 8181 is 99.

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