Answer:
(5, -1)
Step-by-step explanation:
The three coordinates of a triangle are given as:
(5,3), (-5,3), (-5,-1).
To find:
The missing vertex = ?
Solution:
Let us label the vertices:
A (5,3),
B(-5,3),
C(-5,-1).
Let the missing vertex be ([tex]x, y[/tex]).
Let us recall the properties of a rectangle.
The opposite sides of the rectangle are equal and parallel to each other.
Let us consider the side AB, we can see that only x coordinate is changed from A to B.
Let us consider the side BC, we can see that only y coordinate is changed from B to C.
A and B are adjacent vertices.
Similarly the opposite vertices will be C and D.
Same pattern will be followed in CD as that of AB.
x coordinate will be changed by same difference as that of AB.
Change in x coordinate from D to C = [tex]-5-x[/tex]
Change in x coordinate from A to B = [tex]-5-5 =-10[/tex]
Equating them:
[tex]-5-x=-10\\\Rightarrow x = 5[/tex]
Same pattern is followed in BC and AD.
Their change in y coordinate will be same.
[tex]-1-3=y-3\\\Rightarrow y =-1[/tex]
Missing vertex is (5, -1).
Please refer to the attached image for the rectangle.
