Answer:
there are two possible values for "a," which are a = 5 and a = -5, such that the distance between the points (a, 7) and (2a, -5) equals 13.
Explanation:
To find the value of "a" if the distance between the points (a, 7) and (2a, -5) equals 13, you can use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given as:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (a, 7) and (x2, y2) = (2a, -5). The given distance is 13. So, you have:
13 = √((2a - a)^2 + (-5 - 7)^2)
13 = √(a^2 + (-12)^2)
13 = √(a^2 + 144)
Now, square both sides to isolate a:
169 = a^2 + 144
a^2 = 169 - 144
a^2 = 25
Take the square root of both sides:
a = ±√25
a = ±5
So, there are two possible values for "a," which are a = 5 and a = -5, such that the distance between the points (a, 7) and (2a, -5) equals 13.