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
