Question

A rhombus, COAL is centered at the origin. The longer diagonal is on the y-axis and has a

Answer 1

Answer with Step-by-step explanation:

We are given  that

COAL is a rhombus .

CA and LO are the diagonals of rhombus COAL.

CA=27 m

OL=19 m

We know that

Diagonals of rhombus are bisect to each other.

Let P(0,0) be the intersecting point of diagonals

Therefore, CP=PA

LP=PO

Length PO=$\frac{1}{2}LO=\frac{19}{2}=9.5 m$

Length of CP=$\frac{1}{2}PA=\farc{1}{2}(27)=13.5 m$

Let C($0,y_2),O(x_1,0),A(0,y_1) \;and\;L(x_2,0)$.

Distance formula:$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the formula

$CP=\sqrt{(0-0)^2+(0-y_2)^2}=13.5$

$\sqrt{y^2_2}=13.5$

$y_2=\pm 13.5$

C(0,13.5) or (0,-13.5)

$\sqrt{(y_2-y_1)^2}=27$

Substitute the value $y_2=13.5$

$\sqrt{13.5-y_1}=27$

$13.5-y_1=\pm 27$

$y_1=13.5-27=-13.5$

A(0,-13.5)

$13.5-y_1=-27$

$y_1=13.5+27=40.5$

A(0,40.5)

Substitute $y_2=-13.5$

$\sqrt{(-13.5-y_1)^2}=27$

$-13.5-y_1=\pm 27$

$-13.5-y_1=27$

$y_1=-13.5-27=-40.5$

A(0,-40.5)

$-13.5-y_1=-27$

$y_1=-13.5+27=13.5$

A(0,13.5)

$LP=\sqrt{(x_2-0)^2}=9.5$

$\sqrt{x^2_2}=9.5$

$x_2=\pm 9.5$

L(9.5,0) or L(-9.5,0)

$\sqrt{x_2-x_1)^2}=19$

$(9.5-x_1)^2}=19$

$9.5-x_1=\pm 19$

$9.5-x_1=19$

$x_1=9.5-19=-9.5$

$9.5-x_1=-19$

$x_1=9.5+19=28.5$

$(-9.5-x_1)=19$

$-9.5-x_1=\pm 19$

$-9.5-x_1=19$

$x_1=-9.5-19=-28.5$

$-9.5-x_1=-19$

$-9.5+19=x_1$

$x_1=9.5$

O(-9.5,0) or O(28.5,0) or (-28.5,0) or (9.5,0)