Question

A. The distance between two towns P and Q is 2 km. On a

Answer 1

Greetings from Brasil...

The expression that allows you to calculate the distance between two points is:

d(P; Q) = √[(Xq - Xp)² + (Yq - Yp)²]

It is said in the statement of the question that the distance PQ [d(P; Q)] is 2, then

d(P; Q) = 2, P(X; 7) and Q(3; 5)

substituting these values in the expression above....

d(P; Q) = √[(Xq - Xp)² + (Yq - Yp)²]

2 = √[(3 - X)² + (5 - 7)²]

2 = √[(9 - 6X + X²) + (- 2)²]

2 = √[9 - 6X + X² + 4]

2 = √[X² - 6X + 13]     squaring both members

(2)² = (√[X² - 6X + 13])²

4 = X² - 6X + 13

X² - 6X + 13 - 4 = 0

X² - 6X + 9 = 0      solving this 2nd degree equation

Δ = (- 6)² - 4 . 1 . 9

Δ = 0     just 1 root

X' = (- (- 6) + √0)/2.1

X' = 6/2

X' = 3

The distance between two towns P and Q is 2 km. On a

coordinate system, town Phas coordinates (x,7) and Q

has coordinates (3,5). The values of the coordinates are

given in kilometres. Find the value of x.