The line shown has a slope of between point L and point N and between point Q and point S. the image shows two triangles. the hypotenuses are on line c points sqr are: s- (10,10) q-(6,4) r- (10,4) LMN are; N- (4,1) M- (4,-8) L- (-2,-8)
which of the following are true?
A: mn/lm = rs/qr
B: lm/mn = qs/qr
C: lm/ln = qs/qr
D: mn/lm = qr/qs
To find the slopes of the given lines, we can use the formula: slope = (change in y) / (change in x).
The slope of line LM can be found using points L(-2, -8) and M(4, -8):
slope of LM = (-8 - (-8)) / (4 - (-2)) = 0 / 6 = 0
The slope of line LN can be found using points L(-2, -8) and N(4, 1):
slope of LN = (1 - (-8)) / (4 - (-2)) = 9 / 6 = 3/2
The slope of line QR can be found using points Q(6, 4) and R(10, 4):
slope of QR = (4 - 4) / (10 - 6) = 0 / 4 = 0
The slope of line QS can be found using points Q(6, 4) and S(10, 10):
slope of QS = (10 - 4) / (10 - 6) = 6 / 4 = 3/2
Now let's check each statement:
A: mn/lm = rs/qr
slope of mn = 3/2
slope of lm = 0
slope of rs = 3/2
slope of qr = 0
3/2 / 0 is undefined, and 3/2 / 0 is also undefined.
So, the statement A is not true.
B: lm/mn = qs/qr
slope of lm = 0
slope of mn = 3/2
slope of qs = 3/2
slope of qr = 0
0 / 3/2 is equal to 0.
So, the statement B is not true.
C: lm/ln = qs/qr
slope of lm = 0
slope of ln = 3/2
slope of qs = 3/2
slope of qr = 0
0 / 3/2 is equal to 0.
So, the statement C is true.
D: mn/lm = qr/qs
slope of mn = 3/2
slope of lm = 0
slope of qr = 0
slope of qs = 3/2
3/2 / 0 is undefined, and 0 / 3/2 is equal to 0.
So, the statement D is not true.
In summary, the only true statement is C: lm/ln = qs/qr.