1. ## Geometry

Hey guys, first time poster! here are four questions I would like some help on, I'd be grateful if you would show all your steps as to how you got the answer as it would help me better understand. Thanks in advance.

1) What is the equation of a circle centered at the origin and passing through the point (-7,4) ?

2) For the triangle PQR, with P (-10,6), Q(-2,8) and R(3,-2) draw the sketch of the median from R and determine its question.

3) A triangle has vertices at J(-2,2) K(-1,-3) and L(4,1). Show that the line segment joining the mid-point of JK and JL is parallel to KL.

4) The quadrilateral ABCD has vertices A(-5,4) B(4,9) and C(9,0) D(0,-5)

Find the slope.

Find the distance.

2. 1) What is the equation of a circle centered at the origin and passing through the point (-7,4) ?
$\displaystyle r^2 = 4^2 + 7^2 = 65$
$\displaystyle (y - 4)^2 + (x + 7)^2 = 65$
$\displaystyle y^2 - 8y + 16 + x^2 + 14x + 49 - 65 = 0$
$\displaystyle x^2 + y^2 + 14x - 8y - 16 = 0$

2) For the triangle PQR, with P (-10,6), Q(-2,8) and R(3,-2) draw the sketch of the median from R and determine its question.
let X = midpoint of PQ
hence the median = RX
x coordinate of X = (-10 - 2)/2 = -6
y coordinate of X = (6 + 8)/2 = 7
X = (-6, 7)
slope of RX = $\displaystyle \frac{7 + 2}{(-6) - 3}$ = -1
$\displaystyle \frac{y + 2}{x - 3} = -1$
y = -x + 1

3. Originally Posted by Avalon

3) A triangle has vertices at J(-2,2) K(-1,-3) and L(4,1). Show that the line segment joining the mid-point of JK and JL is parallel to KL.
Use the rule for finding a midpoint on a line segment $\displaystyle \frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$