Coordinates of Point H in GH Line

In summary, the coordinates of H can be found by solving the equations \frac{-2+x}{2} \,=\,5 and \frac{8+y}{2} \,=\,-3, which represent the midpoint formula for a straight line GH with coordinates G(-2,8) and H(x,y).
  • #1
brackenwolf
1
0
GH is a straight line.
the coordinates of G are (-2,8)
the midpoint of GH is (5,-3)
work out the coordinates of H
 
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  • #2
Hello and welcome to MHB! :D

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  • #3
brackenwolf said:
GH is a straight line.
the coordinates of G are (-2,8)
the midpoint of GH is (5,-3)
work out the coordinates of H

Formula
The midpoint of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is: [tex]\left(\frac{x_1+x_2}{2},\,\frac{y_1+y_2}{2}\right)[/tex]

We are told that: the midpoint of [tex]G(-2,8)[/tex] and [tex]H(x,y)[/tex] is [tex](5,-3).[/tex]

Hence, we have: .[tex]\frac{-2+x}{2} \,=\,5,\quad \frac{8+y}{2} \,=\,-3[/tex]

Solve the two equations.
 

FAQ: Coordinates of Point H in GH Line

What are coordinates?

Coordinates are numerical values that represent the location of a point in a two-dimensional or three-dimensional space. In most cases, coordinates consist of an x-value and a y-value, which indicate the horizontal and vertical position of a point, respectively.

What is a point?

A point is a specific location in space that has no size or dimension. It is often represented by a dot or a cross. In mathematics, points are used to describe the location of objects or to plot graphs and geometric shapes.

What is the GH Line?

The GH Line is a line that connects point G and point H. It is a straight path that extends infinitely in both directions. The GH Line is often used in geometry to represent a reference line or to divide a shape into two equal parts.

How do I find the coordinates of point H in the GH Line?

The coordinates of point H can be found by using the distance between point G and point H, as well as the slope of the GH Line. Once you have these values, you can use them to calculate the x-value and y-value of point H using the slope-intercept formula.

Why are coordinates important?

Coordinates are important because they allow us to precisely describe the location of objects in space. They are used in a variety of fields, including mathematics, science, navigation, and engineering. Coordinates are also essential in creating maps, graphs, and geometric shapes, and they help us understand the relationships between different points and objects.

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