Exercise 37 Page 407

Let's start by plotting the given 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 ⇒ 4^2+ 6^2=c^2 Finally, we can solve for the hypotenuse c. This is the distance between the points.

4^2+6^2=c^2

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Solve for c

CalcPow

Calculate power

16+36=c^2

AddTerms

Add terms

52=c^2

RearrangeEqn

Rearrange equation

c^2=52

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c= sqrt(52)

UseCalc

Use a calculator

c= 7.211102...

RoundDec

Round to 1 decimal place(s)

c≈ 7.2

Because distances are always non-negative, we only considered the principal root. The points are about 7.2 units apart.