Question

Point B has coordinates ​(​5,​2). The​ x-coordinate of point A is 2 . The distance between point A and point B is 5 units. What are the possible coordinates of point​ A?

Answer 1

Step-by-step explanation:

A(2, x) B(5, 2)

distance between A to B is 5cm

Answer 2

$\sf\small\underline\red{Given:-}$

Point B has coordinates (5,2). The x-coordinate of point A is 2 .The distance between point A and point B is 5 units.

$\sf\small\underline\red{To \: find:-}$

What are the possible coordinates of point A?

$\sf\small\underline\red{Solution:-}$

Point A = (2, y)

Point B = (5, 2)

Distance from A to B = [(2-5)²+(y-2)²] = 5

⟹(-3)² + y²-4y+2 =5

⟹9 + y²-4y+2 =5

⟹y²-4y+11 =5

⟹y²-4y = 5-11

⟹ y²-4y = -6

⟹y²-4y+6 = 0

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

$2-4y+6=0 \\ y^{2}-4y+6=0 \\ y2-4y+6=0 \\a={\color{#c92786}{1}}\\b={\color{#e8710a}{-4}} \\ c={\color{#129eaf}{6}} \\ y= \frac{−(-4)± \sqrt{{-4}^{2} −4 \times 1(6)}}{2 \times 1}$

$= \frac{4+\sqrt{8}}{2}$

No real solutions because the discriminant is negative.The square root of a negative number is not a real number