Coordinate Proofs Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. Use a coordinate proof to show that triangle ABC is scalene. What are the lengths of sides AB , BC , and AC ? (1 point) Responses AB≈8.5, BC≈6.4, and AC≈7.1; therefore, ABC is a scalene triangle. cap A cap b almost equal to 8 point 5 , cap b cap c almost equal to 6 point 4 , and cap A cap c almost equal to 7 point 1 ; therefore, upper A upper B upper C is a scalene triangle. AB≈10.6, BC≈8.1, and AC≈7.1; therefore, ABC is a scalene triangle. cap A cap b almost equal to 10 point 6 , cap b cap c almost equal to 8 point 1 , and cap A cap c almost equal to 7 point 1 ; therefore, upper A upper B upper C is a scalene triangle. AB≈10.6, BC≈6.4, and AC≈7.1; therefore, ABC is a scalene triangle. cap A cap b almost equal to 10 point 6 , cap b cap c almost equal to 6 point 4 , and cap A cap c almost equal to 7 point 1 ; therefore, upper A upper B upper C is a scalene triangle. AB≈3.6, BC≈6.1, and AC≈4.2; therefore, ABC is a scalene triangle. cap A cap b almost equal to 3 point 6 , cap b cap c almost equal to 6 point 1 , and cap A cap c almost equal to 4 point 2 ; therefore, upper A upper B upper C is a scalene triangle. Skip to navigation page 18 of 18 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine if triangle ABC is scalene using a coordinate proof, we need the lengths of sides AB, BC, and AC.

A scalene triangle is defined as a triangle where all sides have different lengths.

1. Calculate the lengths of the sides:

   • Use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
   • Label the coordinates of points A, B, and C as \(A(x_1, y_1)\), \(B(x_2, y_2)\), and \(C(x_3, y_3)\).

2. For each pair of points:

   • Length of AB: \[ AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} \]
   • Length of BC: \[ BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} \]
   • Length of AC: \[ AC = \sqrt{(x_C - x_A)^2 + (y_C - y_A)^2} \]

3. Check the lengths:

   • Once you compute the lengths, check if they are all different.

Based on the multiple choice responses, you would choose the set of side lengths where all three lengths are different.

Since I don't have the specific coordinates for points A, B, and C, I cannot compute the exact lengths. However, once you calculate those lengths, compare them to the given options:

• If the lengths calculated are AB≈8.5, BC≈6.4, and AC≈7.1, then you would select that option stating "therefore, ABC is a scalene triangle."

Repeat this step with the other options until you find the one that proves that triangle ABC is scalene.

Please verify the calculations and select the appropriate response based on the computed lengths.