Determine the coordinates of the unknown vertex or vertices of each figure below. Use variables if necessary.I'm not sure how to find $C$ and $E$.

Kody Whitaker
2022-09-26
Answered

Determine the coordinates of the unknown vertex or vertices of each figure below. Use variables if necessary.I'm not sure how to find $C$ and $E$.

You can still ask an expert for help

maceratorti

Answered 2022-09-27
Author has **10** answers

Opposite sides of a parallelogram are parallel and congruent. Since$\overline{AB}$ lies on the x-axis, it is horizontal. Thus, side $\overline{CD}$ is also horizontal. Since it passes through the point $D(b,c)$, the y-coordinate of point $C$ is $c$. Since $\overline{AB}$ has length $a$, so does $\overline{CD}$ Hence, the $x$-coordinate of point $C$ is $a+b$. Therefore, the coordinates of point $C$ are $(a+b,c)$.

The diagonals of a parallelogram bisect each other. Thus, point $E$ is the midpoint of $\overline{AC}$. Hence, its coordinates are

$(\frac{a+b}{2},\frac{c}{2})$

The diagonals of a parallelogram bisect each other. Thus, point $E$ is the midpoint of $\overline{AC}$. Hence, its coordinates are

$(\frac{a+b}{2},\frac{c}{2})$

asked 2022-07-20

Point $A$ has coordinates $({x}_{1},{y}_{1})$, point $B$ has coordinates $({x}_{2},{y}_{2})$ andpoint $M$ has coordinates $(\frac{{x}_{1}+{x}_{1}}{2},\frac{{y}_{1}+{y}_{1}}{2})$

Prove that $AM=\frac{1}{2}AB$

Prove that $AM=\frac{1}{2}AB$

asked 2022-11-11

Problem picture:

asked 2022-10-21

Find the coordinate of the vertex of the following parabola algebraically.

$y={x}^{2}+14x+41$

$y={x}^{2}+14x+41$

asked 2022-08-04

Choose 3 inequalities that form a system whose graph is the shaded region shown above.

$A.y\le -2\phantom{\rule{0ex}{0ex}}B.y\ge -2\phantom{\rule{0ex}{0ex}}C.7x-4y\ge -13\phantom{\rule{0ex}{0ex}}D.7x+2y\ge 17\phantom{\rule{0ex}{0ex}}E.7x-4y\le -13\phantom{\rule{0ex}{0ex}}F.7x+2y\le 17\phantom{\rule{0ex}{0ex}}G.x\ge -2\phantom{\rule{0ex}{0ex}}H.y\le 2$

$A.y\le -2\phantom{\rule{0ex}{0ex}}B.y\ge -2\phantom{\rule{0ex}{0ex}}C.7x-4y\ge -13\phantom{\rule{0ex}{0ex}}D.7x+2y\ge 17\phantom{\rule{0ex}{0ex}}E.7x-4y\le -13\phantom{\rule{0ex}{0ex}}F.7x+2y\le 17\phantom{\rule{0ex}{0ex}}G.x\ge -2\phantom{\rule{0ex}{0ex}}H.y\le 2$

asked 2022-07-25

8. Graph the reflection of AB in the x-axis

9. Locate a point C on the x-axis such that AC + BC is minimized.

C = (______, 0 )

10. Fill in the values to complete item 8 with matrix multiplication.

9. Locate a point C on the x-axis such that AC + BC is minimized.

C = (______, 0 )

10. Fill in the values to complete item 8 with matrix multiplication.

asked 2022-09-29

If the two tangents drawn from a point $P$ to the parabola ${y}^{2}=4x$ are at right angles then find the locus of $P$.

asked 2022-07-16

In the diagram to the right, point $P$ lies on the line $y=\frac{3}{2}x$ and is one vertex of square $PQRS$. Point $R$ has coordinates $(5,0)$.

a. Find the coordinates of point $P$.

b. If point $R$ lies on line $l$, and line $I$ divides quadrilateral $PQRS$ into two regions of equal area, find the equation for line $l$.

a. Find the coordinates of point $P$.

b. If point $R$ lies on line $l$, and line $I$ divides quadrilateral $PQRS$ into two regions of equal area, find the equation for line $l$.