Question

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

Answer 1

Answer:

$a=-9$

Step-by-step explanation:

The distance between two points can be calculated with the formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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":

$7=\sqrt{(a-(-9)^2+(5-(-2))^2}\\\\7=\sqrt{(a+9)^2+49}$

Square both sides of the equation:

$(7)^2=(\sqrt{(a+9)^2+49}})^2\\\\49=(a+9)^2+49\\\\0=(a+9)^2$

Remember that the Square of a binomial is: $(a+b)^2=a^2+2ab+b^2$.

When a quadratic is the square of a binomial, then the roots are equal.  This is called "Double root".

Therefore:

$a=-9$