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 = -7,8
LM = -7,1

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

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

Answer 1

`m = (4)/(3)` ---- Slope of LK

`m = -(3)/(5)` ---- Slope of LM

`D = 5` ---- Length of LK

`D = √(34)` --- Length of LM

Anthony is incorrect

Explanation:

See attachment for complete question.

From the attachment, we have:

`K = (-4,8)`

`L = (-7,4)`

`M = (-2,1)`

Solving (a): Slope of LK

Slope (m) is calculated as thus:

`m = (y_2 - y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (-4,8)` ----- K

`(x_2,y_2) = (-7,4)` ------ L

`m = (4 - 8)/(-7 - (-4))`

`m = (4 - 8)/(-7 +4)`

`m = (-4)/(-3)`

`m = (4)/(3)`

Slope of LM

Slope (m) is calculated as thus:

`m = (y_2 - y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (-7,4)` ---- L

`(x_2,y_2) = (-2,1)` ------ M

`m = (1 - 4)/(-2 - (-7))`

`m = (1 - 4)/(-2 +7)`

`m = (-3)/(5)`

`m = -(3)/(5)`

Solving (b): Length of LK and LM

Here, we have to calculate the length using distance formula;

Distance (D) is calculated as thus:

`D = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

For LK

`(x_1,y_1) = (-4,8)` ----- K

`(x_2,y_2) = (-7,4)` ------ L

`D = √((-7 - (-4))^2 + (4 - 8)^2)`

`D = √((-7 +4)^2 + (4 - 8)^2)`

`D = √((-3)^2 + (-4)^2)`

`D = √(9 + 16)`

`D = √(25)`

`D = 5`

For LM

`(x_1,y_1) = (-7,4)` ---- L

`(x_2,y_2) = (-2,1)` ------ M

`D = √((-2 - (-7))^2 + (1 - 4)^2)`

`D = √((-2 +7)^2 + (1 - 4)^2)`

`D = √((5)^2 + (-3)^2)`

`D = √(25 + 9)`

`D = √(34)`

`D = 5.83`

The above findings is not enough to conclude if Anthony is correct or incorrect.

We need to calculate the distance of KM using the same formula;

`(x_1,y_1) = (-4,8)` ----- K

`(x_2,y_2) = (-2,1)` ------ M

D is calculated as thus:

`D = √((-2 - (-4))^2 + (1 - 8)^2)`

`D = √((-2 +4)^2 + (-7)^2)`

`D = √((2)^2 + (-7)^2)`

`D = √(4 + 49)`

`D = √(53)`

Base on this, we can conclude that Anthony's claim is incorrect.

The triangle is not an isosceles triangle because no two sides are equal