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Math  /  Geometry

Questionarx Maths 1 A 18 1c1 c 1D 1E1 E Summary Bookwork code: IA Calculator not allowed
What are the coordinates of the point halfway between the origin and point AA on the coordin Zoom

Studdy Solution

STEP 1

What is this asking? Find the coordinates smack-dab in the middle of the origin and point A! Watch out! Don't mix up the x and y coordinates, and remember the origin is at (0,0)(0, 0)!

STEP 2

1. Find the coordinates of point A.
2. Calculate the midpoint.

STEP 3

Looking at the graph, we can see that point A sits right at the intersection of x=12x = 12 and y=12y = 12.
So, the coordinates of point A are (12,12)(12, 12).
We **found** it!

STEP 4

The **midpoint** formula is like finding the average of the x-coordinates and the average of the y-coordinates.
It's like meeting halfway!
The formula is given by (x1+x22,y1+y22). \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right).

STEP 5

Our **first point** is the origin, which has coordinates (0,0)(0, 0).
Let's call these (x1,y1)(x_1, y_1).
Our **second point** is A, which has coordinates (12,12)(12, 12).
Let's call these (x2,y2)(x_2, y_2).

STEP 6

Now, let's **plug these values** into the midpoint formula: (0+122,0+122). \left( \frac{0 + 12}{2}, \frac{0 + 12}{2} \right).

STEP 7

**Simplify** the x-coordinate: 0+122=122=6. \frac{0 + 12}{2} = \frac{12}{2} = 6. **Simplify** the y-coordinate: 0+122=122=6. \frac{0 + 12}{2} = \frac{12}{2} = 6.

STEP 8

So, the **midpoint** is (6,6)(6, 6)!

STEP 9

The coordinates of the point halfway between the origin and point A are (6,6)(6, 6).

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