Answer:
Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units
Step-by-step explanation:
Given points:
[tex]P(-12,-2)[/tex]
[tex]Q(3,6)[/tex]
To determine the distance between points P and Q.
Steps to be carried out:
1) Plot the points P and Q on graph.
2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point [tex]O(3,-2)[/tex]
3) Join PQ thus forming a right triangle POQ.
4) We can find the distance of sides OP and OQ by counting the units between the points.
OP=[tex]|-12-3|=|-15|=15\ units[/tex]
OQ=[tex]|6-(-2)|=|6+2|=8\ units[/tex]
4)Now, we can apply Pythagorean theorem for triangle POQ.
[tex]PQ^2=OP^2+OQ^2[/tex] [ [tex]Hypotenuse^2=Leg1^2+Leg 2^2[/tex]]
[tex]PQ^2=15^2+8^2[/tex]
[tex]PQ^2=225+64[/tex]
[tex]PQ^2=289[/tex]
Taking square root both sides:
[tex]\sqrt{PQ^2}=\sqrt{289}[/tex]
[tex]PQ=17\ units[/tex] [We take only the positive value as distance is always positive.
∴ Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units
