Question

On the coordinate plane shown below, points H and F have coordinates (-2,-3) and (-4,2), respectively. Use the distance formula to determine the straight line distance between points H and F. In your final answer, include all of your calculations.

Answer 1

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Kindly refer this attachment .

Answer 2

Given:

Two coordinates H(-2,-3) and F(-4,2).

To Find:

Distance between points H & F, i.e., the length of straight line HF.

Solution:

Since, we know that the distance between any two points $(x_{1},y_1) \ \& \ (x_2,y_2)$, is given by:

Distance = $\sqrt{ (x_2-x_1)^2 + (y_2-y_1)^2 }$

So, lets compare the given points with these points and put the values in the formula. On comparing, we get:

$x_1 = -2\\x_2 = -4\\y_1 = -3\\\& \ y_2 = 2$

Now, putting these values in the formula, we get

HF = $\sqrt{ [(-4)-(-2)]^2 + [2-(-3)]^2 }$

     $= \sqrt{ (-4+2)^2 + (2+3)^2 }\\ \\= \sqrt{ (-2)^2 + (5)^2 }\\ \\= \sqrt{ 4 + 25}\\ \\= \sqrt{29}$

[We'll only consider the positive value as distance cannot be negative.]

So, the distance between the points H & F, i.e., HF = $\sqrt{29}$ units.