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

`a=-9`

Explanation:

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

`d=√((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=√((a-(-9)^2+(5-(-2))^2)\\\\7=√((a+9)^2+49)`

Square both sides of the equation:

`(7)^2=(√((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`