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## Quadrilateral BECK is known to be a rhombus. Two of the vertices are B(3,5) and C(7,-3). a. Find one slope of diagonal EK b. Find

Question

Quadrilateral BECK is known to be a rhombus. Two of the vertices are B(3,5) and C(7,-3).

a. Find one slope of diagonal EK

b. Find an equation of line EK

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Mathematics
3 months
2021-08-15T07:59:03+00:00
2021-08-15T07:59:03+00:00 1 Answers
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## Answers ( )

Answer:a. The slope of EK is

b. The equation of line EK is y = x –

Step-by-step explanation:The form of the equation of a line is

y = m x + b, whereThe rule of the slope is m = , where

∵

BECK is a rhombus∵ The diagonal is the line that joins two opposite vertices

∵ B and C are opposite vertices in the rhombus

∵ E and K are opposite vertices in the rhombus

∴

BC and EK are the diagonals of the rhombus BECK∵ The diagonals of the rhombus are ⊥ and bisect each other

∴

EK is ⊥ bisector to BC→ Let us find the slope and the mid-point of BC

∵ B = (3, 5) and C = (7, -3)

∴ x1 = 3 and y1 = 5

∴ x2 = 7 and y2 = -3

→ Substitute them in the rule of the slope above to find it

∵ m = = = -2

∴ m = -2

∴

The slope of BC = -2→ To find the slope of EK reciprocal the slope of BC and change its sign

∴ m⊥ =

∴ The slope of EK =

a. The slope of EK is→ Substitute the value of the slope in the form of the equation above

∵ y = x + b

→ To find b substitute x and y in the equation by the coordinates

of a point on the line

∵ The mid-point of BC is the mid-point of EK

∵ The mid-point of BC = () = () = (5, 1)

∴

The mid-point of EK = (5, 1)→ Substitute x by 5 and y by 2 in the equation

∵ 1 = (5) + b

∴ 1 = + b

→ Subtract from both sides

∴ = b

→ Substitute the value of b in the equation

∵ y = x +

∴ y = x –

b. The equation of line EK is y =x –