5. Show that A(-4, - 7), B(-1, 2), C(8, 5) and
D(5, - 4) are the vertices of a parallelogram.
7) B(-1,2), C(8,5) and
Answers
Answer:
you should prove your self.
Step-by-step explanation:
take a graph paper and draw the x axis and y axis. point all the points in graph paper.draw lines from a point to other points. measure the opposite sides of the quadrilateral. if the measures of two opposite sides are same then it is a parallogram.
Answer:
The given points are not vertices of parallelogram.
Step-by-step explanation:
By distance formula ,
√(x2-x1)^2+(y2-y1)^2
Sides:
A=(-4,-7) B=(-1,2)
AB=√[-1-(-4)]^2 + [2-(-7)]^2
=√(3)^2 + (9)^2
=√9+81
=√90
=3√10 units
B=(-1,2) C=(8,5)
BC=√[8-(-1)^2] + [5-2]
= √(9)^2 + (3)^2
= √81+9
=√90
=3√10 units
C=(8,5) D=(5,-4)
CD=√(5-8)^2+(-4-5)^2
=√(-3)^2+(-9)^2
=√9+81
=√90
=3√10 units
D=(5,-4) A=(-4,-7)
DA=√(-4-5)^2+[-7-(-4)]^2
=√(-9)^2+(-3)^2
=√81+9
=√90
=3√10 units
AB=BC=CD=DA
Diagonals:
A=(-4,-7) C=(8,5)
AC=√[8-(-4)]^2+[5-(-7)]^2
=√(12)^2+(12)^2
=√144+144
=√288
12√24 units
B=(-1,2) D=(5,-4)
BD=√[5-(-1)]^2+(-4-2)^2
=√(6)^2+(6)^2
=√36+36
=√72
=6√12 units
BD is not equal to BD
Since, all the sides are equal and the diagonals are unequal.
Therefore,its not a parallelogram..
But it satisfies the requirements of rhombus , therefore it's a rhombus.
