Question

answer all the questions please please please please please please please please​

Answer 1

Answer:

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1) (-3,10) ; (6 , -8) divided by (-1 , 6)

$x = \frac{mx1 + nx2}{m + n} \\ - 1 = \frac{ - 3m + 6n}{m + n} \\ - m - n = - 3m + 6n \\ 2m = 7n \\ \frac{m}{n} = \frac{7}{2}$

m : n = 7 : 2

2) A(2,3) , B (4, k) and C (6, -3) are collinear .

$area \: = \frac{1}{2} (2(k + 3) + 4( - 3 - 3) + 6(3 - k) \\ 0 = 2k + 6 - 12 - 12 + 18 - 6k \\ - 4k = 0 \\ k = 0$

k = 0

3) A ( 1,7) ; B (4,2) ; C (-1,-1) ; D(-4,4)

$ab = \sqrt{(4 - 1) {}^{2} + (7 - 2) {}^{2} } \\ ab = \sqrt{9 + 25} \\ ab = \sqrt{34 } \\ \\ bc = \sqrt{(4 + 1) {}^{2} + (2 + 1) {}^{2} } \\ bc = \sqrt{25 + 9} \\ bc = \sqrt{34} \\ \\ cd = \sqrt{( - 4 + 1) {}^{2} + (4 + 1) {}^{2} } \\ cd = \sqrt{9 + 25} \\ cd = \sqrt{34} \\ \\ ad = \sqrt{( - 4 - 1) {}^{2} + (7 - 4) {}^{2} } \\ ad \: = \sqrt{25 + 9} \\ ad = \sqrt{34}$

Therefore it is a square ...

4)

$ab = ac \\ ( x - 7) + (y - 1) = (3 - x) + (5 - y) \\ x - 7 + y - 1 = 3 - x + 5 - y\\ 2x + 2y = 8 + 8 \\ x + y = 8$

5 )

$ac \: = \sqrt{34} \\ \\ bd = \sqrt{72} \\ \\ area \: = \sqrt{52}$

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