Answer:
The possible values of a is 43
Step-by-step explanation:
Using the formula for calculating the distance between 2 points.
D = √(x2-x1)²+(y2-y1)²
Given
D = 45 units
The coordinates Q(–1, a) and P(3,2)
45 = √(3-(-1))²+(-2-a)²
45 = √4²+(-2-a)²
45 = √16+(-2-a)²
45² = 16+(-2-a)²
45² = 16+4+4a+a²
45² = 20+4a+a²
a²-4a+20-2025 = 0
a²+4a-2005 = 0
a = -4±√16+4(2005)/2
a = -4±√16+8020/2
a = -4±√8036/2
a = -4±90/2
a = -4+90/2
a = 86/2
a = 43
