plss helpp its due tmr and i dont really get ittt

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darkslauerqkwen darkslauerqkwen

15-07-2022
Mathematics

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plss helpp its due tmr and i dont really get ittt

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MrRoyal MrRoyal · Answer 1 · 2022-07-17T16:07:04+02:00

The orthocenter of the triangles ABC are (2, 0) and (3, 3)

How to determine the orthocenter?

Question 8

The coordinates are given as:

A(2,0); B(2, 4); C(6,0)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 4)/(6 - 2)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1) + y1

Where:

(x1, y1) = (2,0)

So, we have:

y = 1(x - 2) + 0

y = x - 2

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 0)/(6 - 2)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (2,4)

So, we have:

x = 2

Substitute x = 2 in y = x - 2

y = 2 - 2

y = 0

So, we have:

(x, y) = (2, 0)

Hence, the orthocenter of ABC is (2, 0)

Question 9

The coordinates are given as:

A(1,1); B(3, 4); C(6,1)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 4)/(6 - 3)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1) + y1

Where:

(x1, y1) = (1,1)

So, we have:

y = 1(x - 1) + 1

y = x

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 1)/(6 - 1)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (3,4)

So, we have:

x = 3

Substitute x = 3 in y = x

y = 3

So, we have:

(x, y) = (3, 3)

Hence, the orthocenter of ABC is (3, 3)

How to solve for x?

Question 18 - 20

Line 2x and x+ 3 are congruent lines

So, we have:

2x = x +3

Solve for x

x= 3

Line 3x and 2x + 5 are congruent lines

So, we have:

3x = 2x +5

Solve for x

x = 5

Line 2x - 3 and x + 2 are congruent lines

So, we have:

2x - 3 = x + 2

Solve for x

x = 5

Question 21 - 23

Line x + 5 and 3x + 7 are congruent lines

So, we have:

x + 5 = 3x + 7

Solve for x

x = -1

Line x + 6 and 5x - 4 are congruent lines

So, we have:

x + 6 = 5x - 4

Solve for x

x = 2.5

Line x + 8 and 5x + 7 are congruent lines

So, we have:

x + 8 = 5x + 7

Solve for x

x = 1/4