Question

1. multiple choice 5 points what is the equation of the line that is parallel to the line y = - 1/3x + 4 and passes through the point (6,5)? y = - 1/3x + 3 y = - 1/3x + 7 y = 3x - 13 y = 3x + 5 20. multiple choice 5 points the coordinates of mid - point m and endpoint q of a segment are m(-7,8) and q(-19,30). find the coordinates of the other endpoint. (-31,52) (-13,19) (5,-14) (15,-4)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the mid - point $M(-7,8)$ and one endpoint $Q(-19,30)$, and the other endpoint be $P(x,y)$.

Step2: Solve for x - coordinate

We have $\frac{x+( - 19)}{2}=-7$. Cross - multiply: $x-19=-14$. Then $x=-14 + 19=5$.

Step3: Solve for y - coordinate

We have $\frac{y + 30}{2}=8$. Cross - multiply: $y+30 = 16$. Then $y=16 - 30=-14$.

Answer:

$(5,-14)$