Question

if the point (4, 0), (7, 3)and (k, 5) lies on the same line, what is the value of k? (5,,, 8,,9,,10).​

Answer 1

Step-by-step explanation:

Given: (4, 0), (7, 3)and (k, 5)

To find: if the given points lies on the same line, what is the value of k?

1) 5

2) 8

3) 9

4) 10

Solution:

Tip: Area of triangle made by joining these points is zero.

Step 1: Write formula to find Area of triangle.

Let A(x1,y1), B(x2,y2) and C(x3,y3) are forming a triangle, then

$Ar( \triangle \: ABC) = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y&1) + x_3(y_1 - y_2)|$

Step 2: Put the values of given point and set area to zero.

Because these points are lying in a line, so triangle can't be formed. Thus, area of triangle is equal to zero.

$\frac{1}{2} |4(3 - 5) + 7(5 - 0) + k(0 - 3)| = 0$

on simply

$|4( - 2) + 7(5) + k(- 3)| = 0$

or

$| - 8+ 35 - 3k| = 0$

or

$|27 - 3k| = 0$

or

$3k = 27$

$\bf \red{k = 9 }$

Final answer:

If the point (4, 0), (7, 3)and (k, 5) lies on the same line, then value of k is 9.

Option (3) is correct.

Hope it helps you.

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