Answer:
[tex]j =2 \pm 3 \sqrt{5} [/tex]
Step-by-step explanation:
Use the distance formula:
[tex]d= \sqrt{(x_{1} - x_{2})^{2} - (y_{1} - y_{2})^{2} } [/tex]
Since the two points k(-3,2) and L(3,j) are 9 units apart find j, we substitute d=9 and the coordinates to get:
[tex]9 = \sqrt{( {3 - - 3)}^{2} + (j - 2) ^{2} } [/tex]
[tex]9 = \sqrt{ {6}^{2} + {(j - 2)}^{2} } [/tex]
[tex]81 = 36 + {(j - 2)}^{2} [/tex]
[tex]81 - 36 = {(j - 2)}^{2} [/tex]
[tex]45 = {(j - 2)}^{2} [/tex]
Take square root of both sides:
[tex]j= 2 \pm3 \sqrt{5} [/tex]
