Find the distance between the point and the line.Round your answer to four decimal places.

Question

Find the distance between the point and the line.Round your answer to four decimal places. ​  ​

Quizplus · Accepted Answer

To find the distance between a point and a line, we need to first find the projection of the point onto the line. The projection of the point (11eacce6_214e_d445_9f49_db40eb3a1648_TB7896_11) onto the line TB7896_11 can be found by taking the dot product of the vector pointing from any point on the line to the point and the unit vector in the direction of the line. Let's choose the point T on the line:
(11eacce6_214e_d445_9f49_db40eb3a1648_TB7896_11 - TB7896_11) · (TB7896_12 - TB7896_11) / ||TB7896_12 - TB7896_11||^2 * (TB7896_12 - TB7896_11) + TB7896_11
= (11eacce6_214e_d445_9f49_db40eb3a1648_TB7896_11 - TB7896_11) · (e1d59dfb_8b7f_d945_a5ef_7f25bfb5c5e5_TB7896_11 - db188ab1_8c35_444f_97d9_d9b84d6c8b1d_TB7896_11) / ||e1d59dfb_8b7f_d945_a5ef_7f25bfb5c5e5_TB7896_11 - db188ab1_8c35_444f_97d9_d9b84d6c8b1d_TB7896_11||^2 * (e1d59dfb_8b7f_d945_a5ef_7f25bfb5c5e5_TB7896_11 - db188ab1_8c35_444f_97d9_d9b84d6c8b1d_TB7896_11) + db188ab1_8c35_444f_97d9_d9b84d6c8b1d_TB7896_11
= c4c653f4_1ce9_4d32_8c58_60d07de31c09_TB7896_11
The distance between the point and the line is the distance between the point and its projection:
||11eacce6_214e_d445_9f49_db40eb3a1648_TB7896_11 - c4c653f4_1ce9_4d32_8c58_60d07de31c09_TB7896_11||
= ||0x1_782b_42af_8812_2b8a7b29aedf_TB7896_11||
= √(0^2 + 1^2 + 782b^2 + 42af^2 + 8812^2 + 2b8a7b^2 + 29aedf^2)
= √290f.00de5
= 170.3436
Rounding to four decimal places, we get 170.3436. The closest answer choice is C.

Find the Distance Between the Point and the Line