For the points P and Q, find (a) the distance d(P, Q) and (b) the...

Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(8,2), Q(3,5)

Accepted Answer

Hello everyone. We are going to take the point A. Being 61 and B being 27 and calculate the length and the midpoint of this line segment. So I'm going to consider a. To be my X one Why 1? So there are little sub numbers just to separate them and B. Two B X two Y two. I'm giving them these titles now so I know where to plug them into my formulas. First is my distance formula. In the distance formula distance equals the square root of X. Sub two minus X. Sub one squared plus Y sub two minus Y sub one squared. So using the numbers from points A. And B. I want to find the distance. So it's the square root of X two is -11 which is six squared plus Y. Sub two which is seven minus Y. Sub one which is one again squared. I'm gonna simplify what's in my parentheses. So I still have the square root now of negative four squared Plus 7 -1 is six squared. So the distance equals the square root of four squared. Sorry negative four squared is 16 Plus six squared is 36. So d. is the square root of 52. And I need to see if I can reduce that. I want to factor out any perfect squares to try to simplify my radical And I believe four times 13 equals 52. So this is the square root of four times the square to Square 2. 4 is two square to 13. Does not simplify. So our distance here is too radical 13 units. So that's part of our solution. Too Radical 13 units. But we're not done yet because we also need to find the midpoint the midpoint. How's the formula X one plus X Sub two divided by two for our X value. And why Sub one plus Y sub two divided by two for our Y value. The midpoint ends up being a point. So the X values will give me six plus two divided by two. The Y values one plus seven divided by two. So our mid 0.6 plus two is 8/2. Um 1-plus 7 is eight also over two. And it looks like when we simplify this, our mid point is the .44. So when I put the two pieces together, my mid point is the .44. My distance is too radical 13 units. And that is answer choice a. Have a nice day.

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For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(8,2), Q(3,5)