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QUESTION 5/10 The Point P with Coordinates (-5,12) Is Plotted in the Coordinate Plane. What Is the Shortest Distance from Point P to

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QUESTION 5/10 The point P with coordinates (-5,12) is plotted in the coordinate plane. What is the shortest distance from point P to the origin (0,0) Enter number only (nounits)Ifyouranswerisnota whole number, then round to the nearest hundredth. 1 point Enteranswer here...

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Cevap

The shortest distance from point \( P(-5,12) \) to the origin \( (0,0) \) is 13.

Daha Fazla

## Step 1The problem asks for the shortest distance from a point \( P(-5,12) \) to the origin \( (0,0) \) in a coordinate plane. The shortest distance between any two points in a plane is a straight line. In this case, the two points are \( P(-5,12) \) and \( (0,0) \).## Step 2We can use the distance formula to calculate the distance between these two points. The distance formula is given by:### \( \sqrt{(x2-x1)^2 + (y2-y1)^2} \)## Step 3Substitute the coordinates of the two points into the formula. Here, , , , and .## Step 4Calculate the distance using the formula:### \( \sqrt{(0-(-5))^2 + (0-12)^2} \)## Step 5Simplify the expression inside the square root:### \( \sqrt{(5)^2 + (-12)^2} \)## Step 6Calculate the squares and add them:### ## Step 7Add the results:### ## Step 8Take the square root of 169 to get the final answer:### 13