5
QuizMultiple Choice

Partitioning a Line Segment — Quiz

Question 5 • Geometry

Which expressions can be used to find the coordinates of the midpoint of line segment P Q with endpoints P 3 comma negative 1 and Q negative 7 comma negative 6 ? Choose three correct answers.

Answer
A
the fraction with numerator negative 1 minus 6 and denominator 2 can be used to find the y -coordinate of the point.
B
the fraction with numerator 3 plus 7 and denominator 2 can be used to find the x -coordinate of the point.
C
1 half times open paren negative 6 minus 1 close paren minus 1 can be used to find the y -coordinate of the point.
D
negative 5 halves minus 1 can be used to find the y -coordinate of the point.
E
1 half times open paren negative 7 minus 3 close paren plus 3 can be used to find the x -coordinate of the point.

Explanation

The midpoint coordinates are the averages of the corresponding endpoint coordinates: x = (3 + (−7))/2 = −2 and y = (−1 + (−6))/2 = −7/2. Choice A gives (−1 − 6)/2 = −7/2, and choice D gives (−5/2) − 1 = −7/2. Choice E gives ½(−7 − 3) + 3 = −2. Choice B omits the negative sign on −7, while choice C does not give the correct y-coordinate.

AI-written and checked against the verified answer.

Previous
Next