Question

Determine as coordenadas do ponto médio do segmento AB quando :

Answer 1

Explicação passo-a-passo:

1)

a)

M(xm, ym)

xm = (1+11)/2 = 12/2 = 6

ym = (7+3)/2 = 10/2 = 5

Portanto, M(6, 5)

b)

xm = (-2 - 4)/2 = -6/2 = -3

ym = (5 - 1)/2 = 4/2 = 2

Portanto, M(-3, 2)

c)

xm = (3 - 2)/2 = 1/2

ym = (-1 + 1)/2 = 0/2 = 0

Portanto, M(1/2, 0)

2)

a = (-1 + 5)/2 = 4/2 = 2

b = (4 + 2)/2 = 6/2 = 3

Portanto, M (2, 3)

3)

$d(ab) =\sqrt{({4 - 0})^{2}+({6 - 4})^{2} } = \sqrt{ {4}^{2} + {2}^{2} } = \sqrt{16 + 4} = \sqrt{20} = 2 \sqrt{5}$

$d(ac) =\sqrt{({4 - 0})^{2}+({3 - 4})^{2}} =\sqrt{ {4}^{2}+({ - 1})^{2} } = \sqrt{16 + 1} = \sqrt{17}$

$d(bc)=\sqrt{({4-4})^{2}+({6-3})^{2} } = \sqrt{ {0}^{2} + {3}^{2} } = \sqrt{9} = 3$

Portanto,

AB =

$2 \sqrt{5}$

AC =

$\sqrt{17}$

BC = 3