If p(2,1) and q(8,1) are vertices of a rectangle which of the following cannot be other vertices of the rectangle
Answers
Step-by-step explanation:
If P(2,1) and Q(8,1) are two of the vertices of a rectangle, which of the following could not be another of the vertices? A(2,8),B(8,2),C(2,−8),D(−2,8),E(8,8).
There are two possibilities - P(2,1) and Q(8,1) may be the vertices representing the endpoints of a side or they may be the vertices representing the endpoints of a diagonal.
It may be seen that PQ is parallel to the X axis and the end points of PQ are (2,1) and (8,1).
Case 1:PQ represents a diagonal of the rectangle.
Since PQ represents a diagonal, the lines passing through any of the two other vertices and either P or Q cannot be perpendicular to PQ.
⇒ The X coordinate of the two other vertices cannot be 2 or 8.
This rules out all the other vertices except D(−2,8).
However, we need two other vertices to complete the rectangle.
⇒PQ does not represents a diagonal of the rectangle.
Case 2:PQ represents a side of the rectangle.
Since PQ represents a side, one of the other two vertices should have 2 as the X coordinate and the other should have 8 as the X coordinate.
Further, both the other vertices should have the same Y coordinate.
There are three other points having the same Y coordinate - A(2,8),D(−2,8) and E(8,8).
Out of these three point D has −2 as the X coordinate and can therefore be eliminated.
⇒ The other two vertices are A(2,8), and E(8,8).
⇒ The points that cannot be a vertex of the rectangle are B(8,2),C(2,−8) and D(−2,8).