The slope of AB is - 3/2. Which statement proves that ΔABC contains a right angle?
We need more information to definitively prove that triangle ABC contains a right angle. Knowing the slope of AB gives us information about the angle that line AB makes with the x-axis, but it does not necessarily tell us anything about the angles within triangle ABC. We would need additional information, such as the slopes or lengths of other sides, or the values of specific angles, to prove that triangle ABC contains a right angle.
To prove that triangle ΔABC contains a right angle, we need to show that the slope of one of its sides is the negative reciprocal of the slope of another side. Here's how to do it:
1. Identify the slopes of AB and another side of ΔABC.
2. Determine if the slopes are negative reciprocals of each other.
3. If the slopes are negative reciprocals, then it proves that ΔABC contains a right angle.
Let's proceed to find the slopes of the sides of ΔABC:
1. Given that the slope of AB is -3/2, we still need to identify the slope of another side. Let's call this side CD.
2. Determine the slope of side CD. Without more information, it is not possible to determine the exact slope of CD.
3. Compute the negative reciprocal of -3/2, which is 2/3. This will be the slope we are looking for in order to prove the right angle.
4. To prove that ΔABC contains a right angle, we need to check if the slope of CD is equal to 2/3.
If you have more specific information regarding the coordinates or other properties of triangle ΔABC, please provide them, and I can assist you further in proving that ΔABC contains a right angle.