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...

## Step 1<br />The 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 \( (0,0) \).<br /><br />## Step 2<br />We can use the distance formula to calculate the distance between these two points. The distance formula is given by:<br />### \( \sqrt{(x2-x1)^2 + (y2-y1)^2} \)<br /><br />## Step 3<br />Substitute the coordinates of the two points into the formula. Here, \( x1 = -5 \), \( y1 = 12 \), \( x2 = 0 \), and \( y2 = 0 \).<br /><br />## Step 4<br />Calculate the distance using the formula:<br />### \( \sqrt{(0-(-5))^2 + (0-12)^2} \)<br /><br />## Step 5<br />Simplify the expression inside the square root:<br />### \( \sqrt{(5)^2 + (-12)^2} \)<br /><br />## Step 6<br />Calculate the squares and add them:<br />### \( \sqrt{25 + 144} \)<br /><br />## Step 7<br />Add the results:<br />### \( \sqrt{169} \)<br /><br />## Step 8<br />Take the square root of 169 to get the final answer:<br />### 13