Exercise 1 Page 520

We are given a figure.

Here we want to find the distance from point E to FH. Recall that the distance from a point to a line is defined as the shortest distance. This is going to be the segment that runs perpendicular to FH. Therefore, we can disregard EF and EH.

To find the distance between E and FH, we have to use the Distance Formula. Let's recall the Distance Formula.

Distance Formula

Given two points A(x_1, y_1) and B(x_2, y_2) on a coordinate plane, their distance d is given by the following formula. d=sqrt((x_2-x_1 )^2+(y_2-y_1 )^2)

Therefore, we will use two points E and G to find the distance between point E and the line. We will substitute x- and y-values of the points into the formula and simplify it. Let's do it.

d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( 1,2) & ( - 4,- 3)

d=sqrt(( 1-( - 4))^2+( 2-( - 3))^2)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

d=sqrt((1+4)^2+(2+3)^2)

AddTerms

Add terms

d=sqrt(5^2+5^2)

CalcPow

Calculate power

d=sqrt(25+25)

AddTerms

Add terms

d=sqrt(50)

We found the distance between the point and the line as sqrt(50).