Triangle ABC has been rotated 90° to create triangle DEF. Write the equation, in slope-intercept form, of the side of triangle ABC that is perpendicular to segment EF. You must show all work to receive credit.

Proved: BC and EF have opposite and reciprocal slopes

Step-by-step explanation:

Two lines with slopes that are negative reciprocals of each other are said to perpendicular to each other.

Let m subscript 1 = m1

m subscript 2 = m2

So if m1 is the slope of the 1st (∆ABC)

m2 is the slope of the 2nd (∆DEF)

For both lines to be perpendicular,

m1×m2 = -1

So, the slope of the perpendicular line (DEF) is the negative reciprocal of the slope of the original line (ABC).

The diagram of the question can be found at

Find attached the diagram.

From the diagram, the coordinates of the line segments BC and EF:

B(4,5) C(1,2)

E(5,-4) F(2,-1)

The slope of each of these lines:

m1 = (change in y)/(change in x)

= (2-5)/(1-4) = -3/-3

m1 = 1

m2 = (change in y)/(change in x)

= [-1-(-4)]/(2-5) = (-1+4)/(-3)

m2 = 3/-3

m2 = -1

m2 = negative reciprocal of m1

m2 = -1/1 = -1

From the solution, the slope of BC is the opposite reciprocal of EF.

Therefore, BC and EF have opposite and reciprocal slopes.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.