✒️DISTANCES
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[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]
- What type of triangle is formed by the vertices P(-2, 1), Q(3, 2), and R(0, -2)
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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]
[tex] \qquad \Large \:\: \rm Scalene \: Triangle [/tex]
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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
» Find the distances between all of these points connected indicating as the sides of the triangle using the distance formula.
[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2\,}} \end{align} [/tex]
Find side PQ: Find the distance between (-2, 1) and (3,2)
- [tex] PQ = \sqrt{(3-(\text-2))^2 + (2-1)^2 \,} [/tex]
- [tex] PQ = \sqrt{(3+2)^2 + (2-1)^2 \,} [/tex]
- [tex] PQ = \sqrt{(5)^2 + (1)^2 \,} [/tex]
- [tex] PQ = \sqrt{25 + 1\,} [/tex]
- [tex] PQ = \sqrt{26\,} [/tex]
Find side QR: Find the distance between (3,2) and (0,-2)
- [tex] QR = \sqrt{(0-3)^2 + (\text-2-2)^2\,} [/tex]
- [tex] QR = \sqrt{(\text-3)^2 + (\text-4)^2\,} [/tex]
- [tex] QR = \sqrt{9 + 16\,} [/tex]
- [tex] QR = \sqrt{25\,} [/tex]
Find side RP: Find the distance between (0,-2) and (-2, 1)
- [tex] RP = \sqrt{(\text-2-0)^2 + (1-(\text-2))^2\,} [/tex]
- [tex] RP = \sqrt{(\text-2-0)^2 + (1+2)^2\,} [/tex]
- [tex] RP = \sqrt{(\text-2)^2 + (3)^2\,} [/tex]
- [tex] RP = \sqrt{4 + 9\,} [/tex]
- [tex] RP = \sqrt{13\,} [/tex]
» Since all of the sides have different lengths, then this kind of triangle is an Scalene Triangle
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