Question

GEOMETRY

EXTRAPOINTS

What is the converse of the following conditional?
If a point is in the fourth quadrant, then its coordinates are negative.

Select one:
a. If a point is in the fourth quadrant, then its coordinates are negative.
b. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
c. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
d. If the coordinates of a point are negative, then the point is in the fourth quadrant.

Answer 1

Answer: Choice D

The general format for a conditional is "If P, then Q". The P and Q are placeholders for phrases or expressions. Think of them as empty boxes and inside the boxes you'll place words or a sentence (or sometimes math symbols as well). To form the converse of that template, we simply swap P and Q to get "If Q, then P". In our case,

P = point is in the fourth quadrant

Q = coordinates are negative

so that's how we end up with the answer "If the coordinates of a point are negative, then the point is in the fourth quadrant"

Answer 2

The converse of a conditional statement interchanges the hypothesis and the conclusion.

Here, the conditional statement is: "If a point is in the fourth quadrant, then its coordinates are negative."

To form the converse, we interchange the 'if' part (condition or hypothesis) and the 'then' part (conclusion or result). Hence, the converse of the given conditional statement would be "If its coordinates are negative, then a point is in the fourth quadrant."

So, the correct choice is option d: "If the coordinates of a point are negative, then the point is in the fourth quadrant."