Question

Find the lengths and slopes of the diagonals to name the parallelogram. Choose the most specific name. E (-2, -4), F(0, -1), G(-3. 1) H(-5, -2) Note: Be prepared to explain your answer to this type of question on the test using length and slope. a) Rectangle b) Triangle c) Rhombus d) Square ---------------------------------------------------------------------------------------------------------------------------- What would prove the parallelogram PWRS is a rhombus? P(-1, 3), Q(-2, 5), R(0, 4), S(1, 2) a)Length of QR is 2.2 and slope of QR is -2 b) Slope of QR and PS is -2 and Slope of RS and QP is -1/2 c) Length of QS and PR is 4.2 d) Length of QR and PS is 2.2 and Length of RS and QP is 2.2

Answer 1

Answer:

1) d) Square

2) Proofs that PWRS is a rhombus are

Length of QS ≠ PR and

Slope of segment QR and PS is -1/2 and Slope of segment RS and QP is -2.

Step-by-step explanation:

The given points (x, y) of the parallelogram are;

E(-2, -4), F(0, -1), G(-3, 1), H(-5, -2)

The slope, m, of the segments are found as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

By computation, the slope of segment EF = 1.5

The slope of segment FG = -0.67

The slope of segment GH = 1.5

The slope of segment HE = -0.67

Therefore, EF is parallel to GH and FG is parallel to HE

The length of the sides are;

$\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

By computation, the length of segment EF = 3.61

The length of segment FG = 3.61

The length of segment GH = 3.61

The length of segment HE = 3.61

The diagonals are;

EG and FH

The length of segment EG = 5.099

The length of segment FH = 5.099

Therefore, the diagonals are equal and the parallelogram is a square

2) The given dimensions are;

P(-1, 3), Q(-2, 5), R(0, 4), S(1, 2)

A rhombus has all sides equal

The length of segment PQ = 2.24

The length of segment QR = 2.24

The length of segment RS = 2.24

The length of segment PS = 2.24

The diagonals are;

QS and PR

The length of segment QS = 4.24

The length of segment PR = 1.41

The slope of segment QR = -0.5

The slope of segment PS = -0.5

The slope of segment RS = -2

The slope of segment QP = -2

Therefore, QS≠QR the parallelogram is a rhombus

The correct option ;

Length of QS ≠ PR and

Slope of segment QR and PS is -1/2 and Slope of segment RS and QP is -2.

Where there are acute angles in parallelogram PQRS, then the correct option is d) Length of QR and PS is 2.2 and Length of RS and QP is 2.2