Exercise 32 Page 419

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

We know the vertical and horizontal measures of the triangle. We can use these measures as the legs in the Pythagorean Theorem. a^2+ b^2=c^2 ⇒ 10^2+ 5^2=c^2 Finally, we can solve for the hypotenuse c. This is the distance between the points. Remember that distances are always non-negative, so we will only use the positive square root.

10^2+5^2=c^2

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Solve for c

CalcPow

Calculate power

100+25=c^2

AddTerms

Add terms

125=c^2

RearrangeEqn

Rearrange equation

c^2=125

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(c^2)=sqrt(125)

CalcRoot

Calculate root

c=sqrt(125)

UseCalc

Use a calculator

c=11.180339...

RoundDec

Round to 1 decimal place(s)

c≈ 11.2

The points are approximately 11.2 units apart.