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The points 1 , B and ( are (9 , 8) , ( 12, 4) and (4, - 2) respectively
(a) Find
(1)
the gradient of the line through d and B
(¡i)
the equation of the line through C which is parallel to AB
(b) Calculate the length of the line segment
(i)
[21
(11)
BC
[21
(c) Show that AB is perpendicular to BC 121
(d) Calculate the area of triangle ABC
[1)

The points 1 B and are 9 8 12 4 and 4 2 respectively a Find 1 the gradient of the line through d and B i the equation of the line through C which is parallel to class=

Respuesta :

lavisteresther

Answer:

a.i.

[tex]mab = \frac{ya - yb}{ xa - xb} = \frac{8 - 4}{9 - 12} = \frac{4}{ -3} [/tex]

a.ii.

[tex]mc = mab = \frac{4}{ - 3} \\ (y - y1) = m(x - x1) \\ y - ( - 2) = \frac{4}{ - 3}(x - 4) \\ y + 2 = \frac{4}{ - 3}x + \frac{16}{3} \\ y = \frac{4}{ - 3} x + \frac{16}{ 3} - 2 \\ y = \frac{4}{ - 3}x + \frac{10}{3} [/tex]

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