Mathematics, 07.06.2020 14:57 AbbyRichter

find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,3) and the base is on the line x=0

Answers: 3

Show answers

Answers

Answer from: DaFuzzyDude

An isosceles right triangle has two equal length legs and the hypotenuse side as its base

The equation of the sides of the isosceles right triangle are;

x = 0 (equation of the base)

y = 1 - x

y = x + 5

The reason for arriving at the above equations are as follows:

The given parameters of the isosceles right triangle are:

The coordinate of the vertex of the triangle = (-2, 3)

The base of the triangle, x = 0

The required parameter:

The equation of the sides of the isosceles triangle

Strategy:

Define the terms and relate the given information with the given term definitions

Solution:

The base of an isosceles triangle is the side that form the equal base angles with the two equal sides of the triangle

In an isosceles right triangle, the two equal sides of the right triangle are the legs of the right triangle, and therefore, the base of the triangle is the hypotenuse side

The base angles of an isosceles right triangle, $\theta _b$ = 45°

The altitude of the triangle, y = (0 - (-2) = 2

The altitude is a perpendicular bisector of the base, therefore;

$tan(\theta _b) = \dfrac{Altitude}{\dfrac{1}{2} \times Base \ length }$

Therefore;

$Base \ length = \dfrac{Altitude}{\dfrac{1}{2} \times tan(\theta _b)}$

We get:

$\mathbf{Base \ length} = \dfrac{2}{\dfrac{1}{2} \times tan(45^{\circ})} \mathbf{= 4~}$

The coordinate of the midpoint of the base is the horizontal line from the vertex to the base, and therefore, the coordinate of the midpoint of the base is x = 0, and y = 3 = (0, 3)

The base is 4 units long and half the base length = 4/2 = 2 units

The coordinates of vertex at the base is given by adding or subtracting 2 from the y-coordinates of midpoint of the base as follows;

Vertex coordinates at the base = (0, 3 + 2) = (0, 5), and (0, 3 - 2) = (0, 1)

The slope, m₁, of the side, s₁, with endpoints (-2, 3), and (0, 1), is found as follows;

m₁ = (1 - 3)/(0 - (-2)) = -1

Therefore, the equation of the side s₁ is (y - 1) = -1·(x - 0), which gives;

y = -x + 1

The slope, m₂, of the side, s₂, with endpoints (-2, 3), and (0, 5), is found as follows;

m₂ = (5 - 3)/(0 - (-2)) = 1

Therefore, the equation of the other side s₂ is (y - 5) = 1·(x - 0), which gives;

y = x + 5

The equation of the sides are; x = 0 (given), y = 1 - x, and y = x + 5

Learn more about finding the equation of a line here:

link

find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,3) and the

Answer from: ineedhelpwhomework

$\large \boxed{y = x + 5; y = -x + 1}$

Step-by-step explanation:

This is an isosceles right triangle, so triangles ABD and CBD are congruent.

∠ ABD = ∠CBD = 45°

The slope of BC = tan(45°) = 1, and

The slope of BA = tan(-45°) = -1.

1. Equation of BC

The point-slope formula for a straight line is

y - y₁ = m(x - x₁)

x₁ = -2; y₁ = 3; m = 1

Substitute the values

$\begin{array}{rcl}y - 3 & = & 1(x - (-2))\\y - 3 & = & x + 2\\y & = & x + 5\\\end{array}\\\text{The equation for the line is $\large \boxed{\mathbf{y = x + 5}}$}$

2. Equation of BA

x₁ = -2; y₁ = 3; m = -1

Substitute the values

$\begin{array}{rcl}y - 3 & = & -1(x - (-2))\\y - 3 & = & -1(x + 2)\\y - 3 & = & -x - 2\\y & = & -x +1\\\end{array}\\\text{The equation for BA is $\large \boxed{\mathbf{y = -x + 1}}$}$

Answer from: Quest

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%

Answer from: Quest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

$\frac{ab}{bc} =\frac{ad}{ab}$

now, we can cross multiply

and we get

$ab\timesab=ad\times bc$

$ab^2=ad\times bc$

so, this could be step to prove it

Seth is using the figure shown below to prove pythagorean theorem using triangle similarity: in the

Another question on Mathematics

Mathematics, 21.06.2019 18:30

Over the last 8 nights, elyse earned the following in tips: {105, 120, 84, 95, 100, 132, 140}. if she earns $140 a night for the next four nights, which measure of center would increase more, the mean or median?

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

1. which of the following algebraic equations is equivalent to ? x^n = a a^n = x a^x = n x^a = n 2. 16^1/4= 1/2 2 4 3. (-36)^1/2= -6 1/6 no real number 4. 8^2/3= 4 8 16√2 )^5/2= 7,776 1/7,776 no real number 6. m ^ the square root of a^2m simplified is: 7. the square root of 3^3 times the square root of 2 simplified and in radical form is:

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

What is the gcf of 20c^3-5c^4+30c^6

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

Taber invested money in an account where interest is compounded every year.he made no withdrawals or deposits. the function a(t)=525(1+0.05)^t represent the amount of money in the account after t years. how much money did taber origanally invested?

Answers: 1

Answer

You know the right answer?

find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,3) and the...

Questions