What is the orthocenter of the triangle with two altitudes given by the lines x = -1 and y = x + 1. : (0, -1) (-1, -2) (-1, 0) none of these

Orthocenter is the point of concurrence of the altitudes of the triangle.

This means Orthcenter is the point where the altitudes intersect.

Here one altitude is x = -1

The other altitude is y = x + 1

Substituting x = -1 in y = x + 1

We get

y = -1-1=0

Hence the point of intersection of the altitudes is (-1,0)

The orthocenter of the triangle whose altitudes are x = -1 & y = x+1 is (-1,0)

(-1,0) which is Option c) or the third option is the right answer.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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