<em>Greetings from Brasil...</em>
The expression that allows you to calculate the distance between two points is:
<h2>d(P; Q) = √[(Xq - Xp)² + (Yq - Yp)²]</h2>
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] <em> squaring both members</em>
(2)² = (√[X² - 6X + 13])²
4 = X² - 6X + 13
X² - 6X + 13 - 4 = 0
X² - 6X + 9 = 0 <em>solving this 2nd degree equation</em>
Δ = (- 6)² - 4 . 1 . 9
Δ = 0 <em>just 1 root</em>
X' = (- (- 6) + √0)/2.1
X' = 6/2
<h2>X' = 3</h2>
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.
