SOLUTION: find the possible values of a if the points with the given coordinates are the indicated distance apart. (4,7),(a,3); d=5 (5,a), (6,1); d= square root of 10 (6,-3),(-3,a);

Algebra ->  Coordinate-system -> SOLUTION: find the possible values of a if the points with the given coordinates are the indicated distance apart. (4,7),(a,3); d=5 (5,a), (6,1); d= square root of 10 (6,-3),(-3,a);      Log On


   



Question 44973: find the possible values of a if the points with the given coordinates are the indicated distance apart.
(4,7),(a,3); d=5
(5,a), (6,1); d= square root of 10
(6,-3),(-3,a); d= square root of 130

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Use Distance Formula: d+=+sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29
(4,7),(a,3); d = 5
d+=+sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29
5+=+sqrt%28%284+-+a%29%5E2+%2B+%287+-+3%29%5E2%29
25+=+%284+-+a%29%5E2+%2B+16
9+=+%284+-+a%29%5E2
3+=+4+-+a or -3+=+4+-+a
-1+=+-a or -7+=+-a
-1+=+-a or -7+=+-a
1+=+a or 7+=+a
(1,3) or (7,3)
(5,a), (6,1); d = square root of 10
d+=+sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29
sqrt%2810%29+=+sqrt%28%286+-+5%29%5E2+%2B+%281+-+a%29%5E2%29
9+=+%281+-+a%29%5E2
3+=+1+-+a and -3+=+1+-+a
2+=+-a and -4+=+-a
-2+=+a and 4+=+a
(6,-3),(-3,a); d = square root of 130
d+=+sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29
sqrt%28130%29+=+sqrt%28%28-3+-+6%29%5E2+%2B+%28a+%2B+3%29%5E2%29
49+=+%28a+%2B+3%29%5E2
7+=+a+%2B+3 and -7+=+a+%2B+3
4+=+a and -10+=+a
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+a%29+