Exercise 11 Page 417

Let's start by plotting the points on the coordinate plane. We can use the Pythagorean Theorem to find the distance between the points! To do so, we first need to draw a right triangle whose hypotenuse is the segment that connects the points.

We know the vertical and horizontal measures of the triangle. We use these measures as the legs in the Pythagorean Theorem. a^2+ b^2=c^2 ⇒ 12^2+ 16^2=c^2 Finally, we can solve for the hypotenuse c. This is the distance between the points. Remember that a side length is always non-negative, so we only need to consider the positive square root.

12^2+16^2=c^2

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Solve for c

CalcPow

Calculate power

144+256=c^2

AddTerms

Add terms

400=c^2

RearrangeEqn

Rearrange equation

c^2=400

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c=sqrt(400)

CalcRoot

Calculate root

c=20

The distance between the points is 20 units.