Question

explain it correctly​

Answer 1

• Three colinear points need the same slope.
• We get two slopes from the given points.

$\boxed{\sf{Slope\;of\;(2,\;5)\;and\;(8,\;8)}}$

$\sf{\implies \dfrac{\Delta y}{\Delta x} =\dfrac{8-5}{8-2} =\dfrac{3}{6} }$

$\sf{\therefore \dfrac{\Delta y}{\Delta x} =\dfrac{1}{2} }$

$\boxed{\sf{Slope\;of\;(4,\;k)\;and\;(8,\;8)}}$

$\sf{\implies \dfrac{\Delta y}{\Delta x} =\dfrac{8-k}{8-4} }$

$\sf{\therefore \dfrac{\Delta y}{\Delta x} =\dfrac{8-k}{4} }$

Hence we get an equation for one variable.

Two slopes need to be equal.

$\sf{\implies \dfrac{8-k}{4} =\dfrac{1}{2} }$

$\sf{\implies 8-k=4}$

$\sf{\therefore k=4}$

Side note:-

• I've attached the reasoning of the slope approach. I approached with the slope, but you can find the solution based on the triangle area formula. H

Answer 2

Three colinear points need the same slope.

We get two slopes from the given points.

$\boxed\red{\sf{Slope\;of\;(2,\;5)\;and\;(8,\;8)}}$

$\sf\red{\implies \dfrac{\Delta y}{\Delta x} =\dfrac{8-5}{8-2} =\dfrac{3}{6} }$

$\sf\red{\therefore \dfrac{\Delta y}{\Delta x} =\dfrac{1}{2} }$

$\boxed\red{\sf{Slope\;of\;(4,\;k)\;and\;(8,\;8)}}$

$\sf\red{\implies \dfrac{\Delta y}{\Delta x} =\dfrac{8-k}{8-4} }$

$\sf\red{\therefore \dfrac{\Delta y}{\Delta x} =\dfrac{8-k}{4} }$

Hence we get an equation for one variable.

Two slopes need to be equal.

$\sf\red{\implies \dfrac{8-k}{4} =\dfrac{1}{2} }$

$\sf\red{\implies 8-k=4}$

$\sf\red{\therefore k=4}$