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

Answer:

$m = \frac{4}{3}$ ---- Slope of LK

$m = -\frac{3}{5}$ ---- Slope of LM

$D = 5$ ---- Length of LK

$D = \sqrt{34}$ --- Length of LM

Anthony is incorrect

Step-by-step 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:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

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

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

$m = \frac{4 - 8}{-7 - (-4)}$

$m = \frac{4 - 8}{-7 +4}$

$m = \frac{-4}{-3}$

$m = \frac{4}{3}$

Slope of LM

Slope (m) is calculated as thus:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

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

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

$m = \frac{1 - 4}{-2 - (-7)}$

$m = \frac{1 - 4}{-2 +7}$

$m = \frac{-3}{5}$

$m = -\frac{3}{5}$

Solving (b): Length of LK and LM

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

Distance (D) is calculated as thus:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

For LK

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

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

$D = \sqrt{(-7 - (-4))^2 + (4 - 8)^2}$

$D = \sqrt{(-7 +4)^2 + (4 - 8)^2}$

$D = \sqrt{(-3)^2 + (-4)^2}$

$D = \sqrt{9 + 16}$

$D = \sqrt{25}$

$D = 5$

For LM

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

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

$D = \sqrt{(-2 - (-7))^2 + (1 - 4)^2}$

$D = \sqrt{(-2 +7)^2 + (1 - 4)^2}$

$D = \sqrt{(5)^2 + (-3)^2}$

$D = \sqrt{25 + 9}$

$D = \sqrt{34}$

$D = 5.83$

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:

$D = \sqrt{(-2 - (-4))^2 + (1 - 8)^2}$

$D = \sqrt{(-2 +4)^2 + (-7)^2}$

$D = \sqrt{(2)^2 + (-7)^2}$

$D = \sqrt{4 + 49}$

$D = \sqrt{53}$

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