Exercise #5: Four points in the plane have coordinates of A
D(7,10). A line is drawn through A and B and a separate
lines AB and CD parallel? Justify your answer.
* A(2,4), B(8,13), C(-3,-5), and
he is drawn through C and D. Are

The lines are parallel

Step-by-step explanation:

Step 1 :

The given 4 points are A(2,4), B(8,13), C(-3,-5),D(7,10)

We need to determine if the lines AB and CD are parallel.

When the slopes of 2 lines are same then the 2 given lines are parallel. Hence we need to find the slopes of the lines passing through the given points

Step 2 :

Slope of line joining AB = (13-4)/(8-2) = 9/6 = 3/2

Slope of line joining CD = (10-(-5))/(7-(-3)) = 15/10 = 3/2

Since the slope of AB is equal to the slope of CD, the  line joining  A and B and the line joining C and D are parallel.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )