Question

i am awarded 50 points on this question

The points A[1,-2], B[2,3], C[k,2] and D[-4,-3] are the vertices of a parallelogram.Find the value of k and the altitude of the parallelogram corresponding to the base AB

Answer 1

Answer:

Using your coords

Work out the gradient of AB and DC

AB = y2 - y1/x2 - x1 = 3 - (-2)/2 - 1 = 5/1

DC = y2 - y1/x2 - x1 = 2 - (-3)/a - (-4) = 2 + 3/a + 4

AC has the same gradient as DC (parallelogram opposite sides)

DC = 5/ a + 4 = 5/1

Cross multiply

5 = 5(a + 4)

5 = 5a + 20

5a = -15

a = -3

C (-3,2)

Height of parallelogram

Using DC

D(-4,-3) C(-3,2)

Distance formula:

√(x2 - x1)^2 + y^2 - y1)^2

√ (-3 - (-4))^2 + (2 - (-3)

√(1)^2 + (5)^2

√ 26

= 5.1 units (1 decimal place)

Answer 2

See the above attachments I hope it will help you^_^


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#HARYANVI THINKER NISHU ❤