Find the possible values for a if the points with the given coordinates are indicated distance apart. Question 31. (-9, -2), (a, 5); d=7

Accepted Solution

Answer: [tex]a=-9[/tex]Step-by-step explanation: The distance between two points can be calculated with the formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] Knowing that the poins are (-9, -2) and (a, 5),  and the distance between these two points is 7, you can substitute values into the formula and solve for "a": [tex]7=\sqrt{(a-(-9)^2+(5-(-2))^2}\\\\7=\sqrt{(a+9)^2+49}[/tex] Square both sides of the equation: [tex](7)^2=(\sqrt{(a+9)^2+49}})^2\\\\49=(a+9)^2+49\\\\0=(a+9)^2[/tex] Remember that the Square of a binomial is: [tex](a+b)^2=a^2+2ab+b^2[/tex]. When a quadratic is the square of a binomial, then the roots are equal.  This is called "Double root". Therefore: [tex]a=-9[/tex]