Question

ABCD is a parallelogram in which B(9,2) and D(5,6) the diagonal AC is inclined at the angle of 45 degree to the x-axis find the equation of diagonal AC

Answer 1

$\textbf{Given:}$

$\text{In parallelogram ABCD, B(9,2) and D(5,6)}$

$\textbf{To find:}$

$\text{The equation of diagonal AC}$

$\textbf{Solution:}$

$\text{We know that,}$

$\textbf{Diagonals of a parallelogram bisect each other}$

$\implies\text{Midpoint of diagonal AC=Midpoint of diagonal BD}$

$\implies\text{Midpoint of diagonal AC}=(\dfrac{9+5}{2},\dfrac{2+6}{2})$

$\implies\text{Midpoint of diagonal AC}=(\dfrac{14}{2},\dfrac{8}{2})$

$\implies\text{Midpoint of diagonal AC}=(7,4)$

$\text{Since the diagonal AC makes an angle 45^{\circ} with x axis,}$

$\text{Slope of diagonal AC}=tan\,45^{\circ}=1$

$\text{To find the equation of the diagonal AC, we use Slope-Point form}$

$y-y_1=m(x-x_1)$

$y-4=1(x-7)$

$y-4=x-7$

$\implies\bf\,x-y-3=0$

$\therefore\textbf{Equation of diagonal AC is x-y-3=0}$

Find more:

Point A(7,-3) and B(1,9), find:

a. Slope of AB.

b. Equation of line perpendicular bisector of the line AB.

c. He value of 'p' of (-2,p) lies on it.

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The vertices of triangle ABC are A(1,1) B(-3,4),C(2,-5) the equation of the altitude through vertex A is​

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Answer 2

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