Question

O. Find the distance between P (10,-7) and Q (7,- 10). Leave your answer in radical form.

Answer 1

Answer:

$3 \sqrt{2}$

Step-by-step explanation:

You can the distance between P(10,-7) and Q(7,-10) by using 'PQ=

$\sqrt{(10 - 7) ^{2} } + \sqrt{ ( - 7 + 10) ^{2} }$

Also, for example the distance between A(a,b) and B(c,d)

is

$\sqrt{(a - c)^{2} } + \sqrt{(b - d) ^{2} }$

Answer 2

Answer:

$\sqrt{18}$ or $3\sqrt{2}$ units.

Step-by-step explanation:

To find the distance between two points, we can use the Distance Formula.

Distance Formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Given:

P (10, -7) ⇒ x₁ = 10, y₁ = -7

Q (7, -10) ⇒ x₂ = 7, y₂ = -10

Substitute the given values into the formula and simplify.

$\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}$

The distance between points P and Q is $\sqrt{18}$ or $3\sqrt{2}$ units.

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