Triangle abc has vertices a(0,6) b(4,6) c(1,3). sketch a graph of abc and use it to find the orthocenter of abc. then list the steps you took to find the orthocenter, including any necessary points or slope you had to derive.

For line B to AC:  y - 6 = (1/3)(x - 4);  y - 6 = (x/3) - (4/3); 3y - 18 = x - 4, so 3y - x = 14

For line A to BC:  y - 6 = (-1)(x - 0);  y - 6 = -x, so y + x = 6

Since these lines intersect at one point (the orthocenter), we can use simultaneous equations to solve for x and/or y:

(3y - x = 14) + (y + x = 6) =>  4y = 20, y = +5;  Substitute this into y + x = 6:  5 + x = 6, x = +1

So the orthocenter is at coordinates (1,5), and the slopes of all three orthocenter lines are above.

The orthocenter of a triangle in the point of concurrency of the altitudes of

a triangle.

Steps to find the orthocenter:

The given vertices are; A(0, 6), B(4, 6), and C(1, 3)

Step 1; Find the slopes of at least two altitudes of the triangle

The slope of an altitude is equal to , where m is the slope of the

opposite side of the triangle.

, the altitude line from C to is line x = 1

, slope of altitude from A to = -1

Step 2: Find the equation of altitude from A to in point and slope form:

The equation of the altitude from A to in point and slope form is

therefore;

y - 6 = (-1)×(x - 0) = -x

y = 6 - x

Step 3: Find the point of intersection of two or the three altitudes

The orthocenter is the point the altitudes intersect, therefore, at the

orthocenter, we have;

y = 6 - x

x = 6 - y

Given that an altitude is the line x = 1, at the point of intersection, (at the

orthocenter) we have;

x = 1 and x = 6 - y by transitive property of equality, we have;

1 = 6 - y

y = 6 - 1 = 5

y = 5

Therefore, at the orthocenter, x = 1, y = 5, the coordinates of the orthocenter is

Learn more here:

link

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows:

you never say the total so we cant find the percentage used for petrol

step-by-step explanation: