Question

If a (6, -1), b(1, 3) and C(k, 8) are three points such that Ab=bc, find the value of k?

Answer 1

Solution

Given :-

• Point , A( 6,-1) , B(1,3) & C(k,8)

Condition :-

• AB = BC

Find :-

• Value of k

Explanation

Using Formula

★ Distance between two point = √[(x-x')² + (y - y')²]

Where,

• P(x,y) & Q(x' , y') are two point

Now, calculate distance between AB

➡ AB = √[(6-1)²+(-1-3)²]

➡ AB = √[5²+(-4)²]

➡ AB = √[25+16]

➡ AB = √41

Now, calculate distance between BC

➡ BC = √[(1-k)²+(3-8)²]

➡ BC = √[(1-k)²+(-5)²]

➡ BC = √[(1-k)²+25]

Now, Using condition

• AB = BC

➡ √41 = √[(1-k)²+25]

Squaring both sides

➡ 41 = (1-k)² + 25

➡ 1² + k² - 2k + 25 = 41

➡ k² - 2k + 26 - 41 = 0

➡ k² - 2k - 15 = 0

➡k² - 5k + 3k - 15 = 0

➡ k(k-5)+3(k-5) = 0

➡(k-5)(k+3) = 0

➡ (k-5) = 0 Or, (k+3) = 0

➡ k = 5 Or, k = -3

Hence

• Value of k be = 5 & -3

________________

Answer 2

Step-by-step explanation:

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