Question

On the coordinate plane shown below, points H and I have coordinates (-2,-3) and (3,2), respectively.

Answer 1

Answer:

$5\sqrt{2}$

Step-by-step explanation:

Here we are given two coordinates and we are required to fin d the distance between them not by using the distance formula but by using Pythagoras theorem.

Let us see how we do that.

We will take the help of graph in this. We draw a line parallel to x axis passing through H (-2,-3) and a vertical line passing through I(3,2)

Let us assume that these two lines intersect at point J whose coordinates will be (-3,-3)

Now using scale of the graph we can see that Distance HJ = 5 units and IJ= 5 units and ΔHIJ makes and Right angle triangle where ∠IJH = 90°

Hence we can apply Pythagoras theorem in this.

$HJ^{2}+JI^{2}=HI^{2}$

$5^2+5^2=HI^{2}$

$HI^{2}=25+25$

$HI^{2}=50\\HI=\sqrt{50}\\HI=\sqrt{25*2}\\HI=5\sqrt{2}$

Please refer to graph in attachment for further clarification.