Coordinate Graph with 2018

Geometry Level 2

In an x y xy -plane graph, there are 3 lines with the following equations:

  • y = 2 x + 0 y = 2x + 0

  • y = 1 x + 8 y = 1x + 8

  • y = 20 x + 18 y = 20x + 18

Apparently when these lines are plotted on the x y xy -plane graph, they form a triangle with each of their sides.

Find the area of this triangle.

Note: Round your answer to the nearest integer.


The answer is 38.

Winston Choo by Winston Choo , 46, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tom Engelsman
Nov 10, 2020

These three lines have intersection points ( x , y ) = ( 8 , 16 ) ; ( − 1 , − 2 ) ; ( − 10 19 , 142 19 ) (x,y) = (8,16); (-1,-2); (-\frac{10}{19},\frac{142}{19}) . The area of the resultant triangle is computed per:

A = ∣ 1 2 ⋅ ∣ 1 8 16 1 − 1 − 2 1 − 10 / 19 142 / 19 ∣ ∣ = 38 . A = |\frac{1}{2} \cdot \begin{vmatrix} 1 & 8 & 16 \\ 1 & -1 & -2 \\ 1 & -10/19 & 142/19 \end{vmatrix} |= \boxed{38}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...