Question

Determine m para que o triângulo ABC seja retangulo em B, sendo A(7,8), B(4,4) e C(m,7)

Answer 1

DAC^2 = DBC^2 + DAB^2

DAC^2 = (Ax - Cx)^2 + (Ay - Cy)^2

DAC^2 = (7 - m)^2 - (8 - 7)^2

DAC^2 = (7)^2 - 2(7)(m) + (m)^2 + (1)^2

DAC^2 = 49 - 14m + m^2 + 1

DAC^2 = m^2 - 14m + 49 + 1

DAC^2 = m^2 - 14m + 50

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DBC^2 = (Bx - Cx)^2 + (By - Cy)^2

DBC^2 = (4 - m) + (4 - 7)^2

DBC^2 = (4)^2 - 2(4)(m) + (m)^2 + (-3)^2

DBC^2 = 16 - 8m + m^2 + 9

DBC^2 = m^2 - 8m + 16 + 9

DBC^2 = m^2 - 8m + 25

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DAC^2 = (Ax - Bx)^2 + (Ay - By)^2

DAC^2 = (7 - 4)^2 + (8- 4)^2

DAC^2 = (3)^2 + (4)^2

DAC^2 = 9 + 16

DAC^2 = 25

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DAC^2 = DBC^2 + DAB^2

m^2 - 14m + 50 = m^2 - 8m + 25 + 25

m^2 - 14m + 50 = m^2 - 8m + 50

- 14m + 50 = - 8m + 50

- 14m + 8m = 50 - 50

- 6m = 0

m = 0
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m = 0