Find the value of x. Round to the nearest tenth.
1 answer:
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Given:
The vertices of a triangle ABC are A( 0, 2), B (2, 5), and C (−1, 7).
To find:
Part A: The length of each side of the triangle.
Part B: The slope of each side of the triangle.
Part C: Classify the triangle.
Solution:
Part A: The vertices of a triangle ABC are A( 0, 2), B (2, 5), and C (−1, 7).
Distance formula:
Using the distance formula, we get
Similarly,
And,
Therefore, the length of each side of the triangle are .
Part B:
Slope formula:
Slope of side AB is:
Slope of side BC is:
Slope of side AC is:
Therefore, the slopes of sides AB, BC, AC are respectively.
Part C:
Product of slopes of AB and BC is:
So, side AB and BC are perpendicular to each other.
Two sides of triangle ABC are equal and one angle is a right angle.
Therefore, the triangle ABC is an isosceles right triangle.