Question

ᴘʟᴇᴀsᴇ sᴏʟᴠᴇ ᴡɪᴛʜ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ. ᴛʜᴇ ᴏɴᴇ ᴡʜᴏ sᴏʟᴠᴇs ᴘᴇʀғᴇᴄᴛʟʏ ᴡɪʟʟ ɢᴇᴛ 20 ᴛʜᴀɴᴋs + ʙʀᴀɪɴʟɪᴇsᴛ

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Answer 1

$\huge\underline\bold\red{AnswEr}$

$D= ( \frac{3 + x1}{ 2} \frac{ - 3 + y1}{2} )\\ \\</p><p>D \ lies \ on \ x+y=4 \\\\ </p><p></p><p>( \frac{3 + x1}{2} + \frac{ - 3 + y1}{2}) = 4 \\ \\ </p><p></p><p>x1 +y1=8..............(i) \\\\</p><p></p><p>slope of AB = \frac{ - 1}{slope(x + y) = 4} \\\\</p><p>= \frac{ - 1}{ - 1} = 1 \\ \\ 1 = \frac{y1 - ( - 3)}{x1 - (3)} \\\\ \implies x1 -3=y1 +3 \\\\ x1 -y1=6..........(ii) \\\\ </p><p>from \ (i) \ and \ (ii) \\\\</p><p>x1 = 7 \\\\ y1 = 1 \\\\</p><p>B (7,1)$

Answer 2

Any point on the line is (t,4−t)

According to the question,

4  

2

+3  

2

 

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∣4t+3(4−t)−10∣

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=1

⇒∣t+2∣=5

⇒t+2=±5

⇒t=3−7

Hence, the required points are (3,1) and (−7,11).