Exercise 19 Page 387

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 ⇒ 3^2+ 4^2=c^2 Finally, we can solve for the hypotenuse c. This is the distance between the points.

3^2+4^2=c^2

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Solve for c

CalcPow

Calculate power

9+16=c^2

AddTerms

Add terms

25=c^2

RearrangeEqn

Rearrange equation

c^2=25

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(c^2)=sqrt(25)

sqrt(a^2)=± a

c=± sqrt(25)

CalcRoot

Calculate root

c=5

Because distances are always non-negative, we can conclude that the points are about 5 units apart.