Question

WILL GIVE BRAINLIEST! Show that diagonals of MNPQ are congruent if M (3, 2), N(3, –1), P(7, –1), and Q(7, 2). Provide your complete solutions and proofs in your paper homework and respond to questions or statements online.

Answer 1

Answer:

Yes the Diagonals are congruent

Step-by-step explanation:

Show that diagonals of MNPQ are congruent if M (3, 2), N(3, –1), P(7, –1), and Q(7, 2)

We are given the coordinates if a quadrilateral.

The first step would be to find the length of the sides of the quadrilateral, using the formula

√(x2 - x1)² + (y2 - y1)²

When given coordinates (x1, y1) , (x2, y2)

M (3, 2), N(3, –1), P(7, –1), and Q(7, 2)

For MN

M (3, 2), N(3, –1),

=√(3 - 3)² + (-1 -2)²

= √0² + -3²

= √9

= 3

For NP

N(3, –1), P(7, –1)

=√(7 - 3)² +(-1 - (-1))²

= √4² + 0²

= √16

= 4

For PQ

P(7, –1), and Q(7, 2)

=√(7 - 7)² +(2 - (-1))²

= √0² + 3²

= √9

= 3

For MQ

M (3, 2),Q(7, 2)

= √(7 - 3)² + (2 - 2)²

= √4² + 0²

= √16

= 4

From the above solution,

We can see that

Side NP = Side MQ

Side PQ = Side MN

Hence this Quadrilateral is as Rectangle

Side PQ = Side MN = Width = 3

Side NP = Side MQ = Length = 4

To find out if their diagonals are congruent we make use of Pythagoras Theorem

Diagonal is the line that divides a quadrilateral into 2 halves

Width 3, Length = 4

= W² +L² = Diagonal ²

= 3² + 4² = D²

= 9 + 16 = D²

= √25 = D

D = 5

Since the Width and Length are the same for the other side, the diagonal would also be equal to 5

Therefore, their diagonals are congruent i.e they are the same