Answer:
- P1P2 = P1P3 = 2√2
- P2P3 = 4
- isosceles right triangle (both)
Step-by-step explanation:
The length of a side can be found using the distance formula:
d = √((x2 -x1)^2 +(y2 -y2)^2)
For P1P2, this gives ...
d = √((0-(-2))^2 +(1-(-1))^2) = √(4+4) = √8
P1P2 = 2√2
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The same ∆x and ∆y apply to P1P3, so we know ...
P1P3 = 2√2
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The lengths of P1P2 and P1P3 are the same, so the triangle is isosceles.
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The length of P2P3 can be found by subtracting the y-coordinates:
P2P3 = 1 -(-3)
P2P3 = 4
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We note that the slope of P1P2 is 2/2 = 1, and the slope of P1P3 is -2/2 = -1. The product of these slopes is (1)(-1) = -1, so we know those lines are perpendicular. The triangle is a right triangle.
