Answer:
Step-by-step explanation:
If it is a parallelogram the opposite sides will a have the same slope.
Using the diagram we see from the coordinates of A and B:
Slope of AB = (5 - -1)/(-1 - -5)
= 6/4
= 3/2.
In the same way
slope of CD = (2 - -4) / (1 - -3)
= 3/2.
So AB and CD can be shown to be parallel.
Similarly the lines BC and AD are parallel.
So the figure is a parallelogram
Finding the perimeter (counting the units between the points):
Perimeter = 2AB + 2BC
By Pythagoras:
AB = sqrt (6^2 + 4^2) = sqrt 52
BC = sqrt (3^2 + 2^2) = sqrt 13
So Perimeter = 2sqrt52 + 2sqrt13
= 4sqrt13 + 2 sqrt13
= 6sqrt13
or 21.63 unit^2 to 2 decimal places.
Area = sqrt52 * perpendicular distance between the lines AB and CD.
X+y=180
they are adjacent angles
x=50
y=130
Answer:
<h2>
m∠M = 123° ; m∠L = m∠N = 90° </h2>
Step-by-step explanation:
A quadrangle LMNP is inscribed in circle which means:
m∠L + m∠N = m∠P + m∠M = 180°
m∠P + m∠M = 180°
57° + m∠M = 180°
m∠M = 123°
m∠L + m∠N = 180° and m∠L + m∠N
m∠L + m∠L = 180°
2×m∠L = 180°
m∠L = 90°
m∠N = m∠L = 90°
