Please help! Using this information, please answer the following questions.

a. Length of RS = √26 Units

b. Length of SP = √50 Units

c. Length of PQ = √26 units

d. Length of RQ = √50 Units

e. Yes , it is a parallelogram.

Step-by-step explanation:

Given,

P(2 , 2) , Q(1 , -3 ) , R( -4 , 2 ) , S( -3 , 7 )

Now,

To find the length of RS, SP , PQ and RQ , we have to use the formula of distance:

Finding the length of RS

R ( -4 , 2) ---> (X1 , y1 )

S( -3 , 7 ) ----> ( x2 , y2 )

RS=

The length of RS = √26 Units

b. Finding the length of SP

S( -3 , 7)----> (X1 , y1 )

P ( 2 , 2 ) ----> ( x2 , y2 )

SP =

The length of SP is √50 units.

c. Finding the length of PQ

P( 2 , 2 ) ------> (x1 , y1 )

Q ( 1 , -3 ) ------> (x2 , y2 )

PQ=

The length of PQ is √26 units

D. Finding the length of RQ

R( -4 , 2 )----> (X1 , y1 )

Q( 1 , -3 )------> (x2 , y2)

RQ=

The length of RQ = √50 units

e. Determining whether the quadrilateral is a parallelogram or not.

Please see the attached picture

Opposite sides are equal.

Now,

P( 2 , 2 )----> (x1 , y1 )

R( -4 , 2 )----> (x2 , y2 )

PR ( Diagonal)

again,

S ( -3 , 7)----> (X1 , y1 )

Q ( 1 , -3)-----> ( x2 , y2)

Diagonals are not equal.

So, it is a parallelogram.

Hope this helps...

Good luck on your assignment...

b

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.