Question

2. Use the following figure to answer the questions.
Anthony claims that Triangle KLM is an isosceles triangle.

(a) Find the slopes of the two lines.
LK =
LM =

(b) Find the length of the two sides.
LK =
LM =

(c) Based on your findings, is Anthony correct? Justify your answer.

Answer 1

explanation:

(a) Slope (m) of a line is given by y/x

m of LK = 4/3

m of LM = 3/5

(b) Length (d) of a line is given by $\sqrt{(x1-x2)^2+(y1-y2)^2}$

l of LK = $\sqrt{(-7+4)^2 + (4-8)^2}$ = $\sqrt{9+16}$ =5

l of LM =$\sqrt{(-7+2)^2 + (4-1)^2}$ =$\sqrt{5^2 + 3^2}$ =$\sqrt{34}$ = 5.83 (approx.)

(c) Since, slopes of two sides are not equal and length of two sides are different, the given triangle cannot be an isosceles triangle. Hence, Anthony is wrong.

Answer 2

Given : Anthony claims that Triangle KLM is an isosceles triangle.

To Find : slopes of the two lines.  LK   and LM

length of the two sides. LK   and LM

is Anthony correct

Solution:

From the figure

K = ( -4 , 8)

L = (- 7 , 4)

M = (-2 , 1)

Slope of LK =  ( 8 - 4)/(-4 -(-7))  = 4/3

Slope of LM = (  1 - 4)/(-2 - (-7)) = -3/5

Slope of KM = ( 1 - 8)/(-2 - (-4))  = -7/2

LK =  √(-4 -(-7))² + (8 - 4)²   = √3² + 4²    = 5

LM  = √(-2 -(-7))²  + (1 - 4)²  = √5² + 3²    = √34 =  5.831

KM = √(-2 -(- 4))² + (1 -8)²   = √2² + 7²    = √53 =  7.28

None of the two sides are equal

Hence Triangle is not isosceles

Triangle is scalene

Anthony is not correct  as triangle is scalene not isosceles

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