Greetings from Brasil...
The expression that allows you to calculate the distance between two points is:
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
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.
The value of x is 3 so that the distance between two towns P and Q is 2 km.
The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:
[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Given that P has coordinates (x,7) and Q has coordinates (3,5). The distance is 2 km, hence:
[tex]2=\sqrt{(5-7)^2+(3-x)^2} \\\\4=(5-7)^2+(3-x)^2\\\\4=4+9-6x+x^2\\\\x^2-6x+9=0\\\\(x-3)^2=0\\\\x=3[/tex]
Hence the value of x is 3.
Find out more at: https://brainly.com/question/2669795
