Question

For the points given​ below, find ​(a​) PQ and ​(b​) the coordinates of the midpoint of PQ.

P(5, 1), Q(9, -8)

PQ=

Answer 1

Explanation:

To find the distance PQPQ between two points P(x1,y1)P(x1​,y1​) and Q(x2,y2)Q(x2​,y2​), you can use the distance formula:PQ=(x2−x1)2+(y2−y1)2PQ=(x2​−x1​)2+(y2​−y1​)2​Given the points P(5,1)P(5,1) and Q(9,−8)Q(9,−8), you can substitute the coordinates into the formula:PQ=(9−5)2+(−8−1)2=16+81=97≈9.8488PQ=(9−5)2+(−8−1)2​=16+81​=97​≈9.8488So, PQ≈9.8488PQ≈9.8488.Now, to find the midpoint of PQPQ, you can use the midpoint formula:Midpoint=(x1+x22,y1+y22)Midpoint=(2x1​+x2​​,2y1​+y2​​)Substituting the coordinates of PP and QQ:Midpoint=(5+92,1−82)=(7,−72)Midpoint=(25+9​,21−8​)=(7,−27​)So, the coordinates of the midpoint of PQPQ are (7,−72)(7,−27​).