## Solve Lesson 30 Page 73 SBT Math 10 – Kite>

Topic

For triangle ABC yes A(3 ; 7), REMOVE(–2 ; 2), OLD(sixty one). Write down the general equation of the altitudes of the triangle ABC.

Solution method – See details

Step 1: Find the VTPT coordinates of the altitudes that are the corresponding opposite sides

Step 2: Find the points that pass through the vertices of the triangle

Step 3: Write the PTTQ of the altitudes when the passing point and the corresponding VTPT are known

Detailed explanation

We have: \(\overrightarrow {AB} = ( – 5; – 5),\overrightarrow {AC} = (3; – 6),\overrightarrow {BC} = (8; – 1)\)

Call AH, BM, CN are the altitudes ofABC. Then:

+ \(AH \bot BC \Rightarrow \) AH pass A and get \(\overrightarrow {BC} = (8; – 1)\) as VTPT so PT: 8xy – 17 = 0

+ \(BM \bot AC \Rightarrow \) BM pass REMOVE and get \(\overrightarrow {{n_1}} = (1; – 2)\) in the same direction as \(\overrightarrow {AC} = (3; – 6)\) as VTPT, so there is PT:

x – 2y + 6 = 0

+ \(CN \bot AB \Rightarrow \) CN pass OLD and get \(\overrightarrow {{n_2}} = (1;1)\) in the same direction as \(\overrightarrow {AB} = ( – 5; – 5)\) as VTPT, so there is PT:

x + y – 7 = 0