Mathematics, 12.12.2019 13:31 iixyloa

The vertices of an isosceles triangle are a(3, 6), b(7, 2), and c(4, 3).

what is the equation of the triangle's line of symmetry?

Answers: 2

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Answers

Check first which sides are equal in length easy to see this using pythagorus theorem. distance between A and B is sqr root of (7-3)^2 +(2-6)^2 = sqr root 32 distance between B and C is sqr root of (4-7)^2 +(3-2)^2 = sqr root 10 distance between C and A is sqr root of (4-3)^2 + (3-6)^2= sqr root 10 so BC = CA so the line of symmetry must go through the other side AB centre of AB is [(7+3)/2, (2+6)/2] = (5,4) and the line must go through the opposite vertex C so finding the line through the 2 points (5,4) and (4,3) y=mx+c m= (4-3)/5-4) =1 y=x+c substitute either point (4,3) gives 3=4+c c=-1 so equation is y=x-1 Check sum: substitute the other point (5,4) 4=5-1 yes so all correct

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

i believe that the answer is

b. y-1=-2(x-4)

hope this !

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The vertices of an isosceles triangle are a(3, 6), b(7, 2), and c(4, 3).

what is the equ...