Question

The following set of coordinates represents which figure? (3, −5), (5, −2), (10, −4), (8, −7)
Parallelogram
Rectangle
Rhombus
Square

Answer 1

Let A(3,-5),B(5,-2),C(10,-4),D(8,-7)
are vertices of a quadrilateral
Here we use distance formula of joining of two points.
A(3,-5)=(x1,y1)
B(5,-2)=(x2,y2)
AB^2=(x2-x1)^2+(y2-y1)^2
=(5-3)^2+(-2+5)^2
=2^2+3^2
=4+9
=13---(1)
BC^2=(10-5)^2+(-4+2)^2
=25+4
=29---(2)
CD^2=(8-10)^2+(-7+4)^2
=4+9
=13--(3)
DA^2=(8-3)^2+(-7+5)^2
=25+4
=29----(4)
Diagonal^2=AC^2
=(10-3)^2+(-4+5)^2
=49+1
=50---(5)
BD^2=(8-5)^2+(-7+2)^2
=9+25
=34---(6)
Here
AB^2=CD^2
BC^2=DA^2
AC^2 not equal to BD^2
Therefore
AB=CD
BC=DA
Opposite sides are equal
AC not equal to BD
Diagonals are not equal
From this
We conclude that
The above vertices shows that
ABCD is a parallelogram