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

-2/

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240