9514 1404 393
Answer:
a = -5 or +1
Step-by-step explanation:
A graphing calculator finds the values of 'a' easily. The points lie on a circle with radius 5 centered at (-2, 6). The points (a, 10) are (-5, 10) and (1, 10). That is the values of 'a' are -5 or 1.
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Often in problems of this nature where the hypotenuse of a triangle is length 5, the legs of the right triangle are 3 and 4. Here, the line y = 10 is 4 units above the point of interest, so the x-coordinates of points 5 units away will be ±3 units from the given point. That is ...
a = -2 ± 3 = -5, +1
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If you don't recognize a 3-4-5 right triangle, and you don't want to graph the problem, you can write the quadratic equation for 'a' using the distance formula:
d² = (a -(-2))² +(10 -6)² . . . . . distance formula d² = (x1 -x2)² +(y1 -y2)²
25 = (a² +4a +4) +16 . . . . . . with numbers filled in, expanded somewhat
a² +4a -5 = 0 . . . . . . . . . . in standard form
(a +5)(a -1) = 0 . . . . . . . factored
The solutions are the values of 'a' that make the factors be 0:
a = -5, a = 1
