Parallelogram esta has vertices e (10, 0), s (14, 3), t (6, 9), and a (2, 6). to calculate its area, jamal will first determine the equation of the line through point e and perpendicular to st. what is the equation of this line in point intercept form?

The vertices of parallelogram ESTA  are E (10, 0), S (14, 3), T (6, 9), and A (2, 6).

As we know ,Area of parallelogram = Base × Height

As base can be determined by using distance formula because coordinates of the vertices are given.

Now to determine perpendicular, we will find the equation of line through E and perpendicular to ST.

Equation of line through S(14,3) and T(6,9) is

⇒4y + 3x =12+42

⇒ 3 x + 4 y=54

Equation of line perpendicular to ST and passing through E(10,0) is

4 x-3 y + k=0

Put x=10, y=0 in above equation is

4×10 -3×0 +k=0

⇒ k= -40

The Equation of line through point E and perpendicular to ST is

4 x-3 y -40=0

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