5 geometry questions?

Question

1.
What is the length of the diagonal of a rectangle with adjacent sides measuring 3 cm and 8 cm?

24.
Write the equation for the line that passes through the point (2, 5) and is perpendicular to the line y = 0.5x - 3.

25.
If C(-3, y) and D(1, 7) lie upon a line whose slope is 2, find the value of y.

26.
What is the relationship between slopes m1 and m2 if the lines are parallel?

29.
In which quadrant would you find the point A (-3, -3)?

Answer 1

length of diagonal = square root of (3^2 + 8^2)
= square root of ( 9+64)
=8.54cm

26.
m1=m2

29.
3rd

25.
m= (7-y)/(1-(-3)) =2
(7-y)/(4)=2
7-y=8
y=7-8= -1

24.
the line is perpendicular then
0.5 * m2 = -1
m2= -2

y=mx+c
5=-2(2)+c
c=5+4
c=9

y=-2x+9

Answer 2

1. Use the pythagorean Theorem Draw a picture.
a^2+b^2=c^2. a=3,b=8
9+64=c^2
73=c^2
c=8.54 cm

24. The slope of y=.5x-3 is .5 or 1/2 so the slope of the line
you want is - 2.

I can think of 3 ways to proceed. I'll show you one. Using the form y=mx+b, substitue -2 for m, 2 for x and 5 for y

5=-2(2)+b
5=-4+b
9=b
Now replace the b with the 9, the m with the 2, and leave the x and y in the equation

y=-2x+9

In standard form this would be 2x-y=9

25. Using the form m= (Y-y)/(X-x) Have point C be (X,Y) and D be (x,y), m=2

2=(y-7)/(-3-1)
2=(y-7)/-4 multiply both sides by -4
-8=y-7 add 7 to both sides
-1=y

26. Parallel lines have the same slope.

29. Fourth Quadrant. Left for the first negative, down for the second.

Answer 3

1.
sqrt( 3^2+8^2)

24. if the line is perpendicular to y=1/2 x -3, then
the slope is equal to -2, so
y-5=-2(x-2)

26. m1=m2

29, the 3rd quadrant

25. y-7=2(x-1),
so if x=-3, then
y-7=2(-3-1)
y=7-8
y=-1

Answer 4

1)
d^2=3^2+8^2
=9+64
=73
d=sqrt(73)

2)
m1=1/2
m2=-2
y-5=-2(x-2)
y=2x+1

3)
y-7=2(x-1)
y=2x+5
y=2(-3)+5
y=-6+5
y= - 1

4)
the slopes are same if the lines are parallel.

5)
x<0, y<0
in the the third quadrant

Answer 5

1.)
3^2 + 8^2 = c^2
9 + 64 = c^2
c^2 = 73
c = sqrt(73)

------------------------

24.)
(2,5), m = -2
5 = -2(2) + b
5 = -4 + b
b = 9

y = -2x + 9

------------------------------

25.)
2 = (7 - y)/(1 - (-3))
2 = (7 - y)/(1 + 3)
2 = (7 - y)/4
7 - y = 8
-y = 1
y = -1

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26.)
m1 = m2

------------------------

29.)
Quadrant I = x,y
Quadrant II = -x,y
Quadrant III = -x,-y
Quadrant IV = x,-y

ANS : Quadrant III

Answer 6

1. 5

24. 1.4

25. 18

26. not equal

29. fourth