Find the orthocenter of △abc. a(2, 3), b(−4, −3), c(2, −3) a. (2, −3) b. (−1, 0) c. (0, −1) d. (−2, 1)

ANSWER



EXPLANATION.

The orthocenter is the point of intersection of any two altitudes of the triangle.

First, you need to determine the slope of each side of the triangle.

△ABC has vertices A(2, 3), B(−4, −3), C(2, −3).





This line has undefined slope, which means it is a vertical line.



The slope of this line is zero, meaning the line is a horizontal line.

This implies that side BC and side AC of the given triangle are perpendicular and will intersect at C since they are the altitudes of triangle ABC.

Hence the orthocentre is



See diagram in attachment.

Let's solve for x.

4x+5y=7

Step 1: Add -5y to both sides.

4x+5y+−5y=7+−5y

4x=−5y+7

Step 2: Divide both sides by 4.

4x/4=−5y+7/4

x=−5/4 y+ 7/4

for the first one x=−5/4 y+ 7/4

3x−2y=−12

Step 1: Add 2y to both sides.

3x−2y+2y=−12+2y

3x=2y−12

Step 2: Divide both sides by 3.

3x/3=2y−12/3

x=2/3y−4

x=2/3y−4

Step-by-step explanation: